Answers
The quadratic function for this problem is given as follows:
Factored form: y = 0.5(x + 1)(x + 8).Standard form: y = 0.5x² + 4.5x + 4.How to define the quadratic function?The roots of the quadratic function in the context of this problem are given as follows:
x = -1.x = -8.Hence the linear factors of the function are given as follows:
x + 1.x + 8.Hence the function is:
y = a(x + 1)(x + 8).
When x = 0, y = 4, hence the leading coefficient a is obtained as follows:
8a = 4
a = 0.5.
Hence the factored form of the function is of:
y = 0.5(x + 1)(x + 8).
The standard form of the function is given as follows:
y = 0.5(x² + 9x + 8)
y = 0.5x² + 4.5x + 4.
More can be learned about quadratic functions at https://brainly.com/question/1214333
#SPJ1
Related Questions
consider a city with two neighborhoods - one rich and one poor - both with equal-sized populations. based on budgetary restrictions, the city employs a police force of 20 officers. let c denote the number of crimes and p the number of
Answers
The variable c indicates the number of crimes in a city with two neighborhoods—one rich and one poor—both of the same size, where the city employs a police force of 20 officers and p represents the number of police officers. Here option C is the correct answer.
To allocate police resources effectively between rich and poor neighborhoods, crime rates, severity, and community policing should be considered to ensure the safety and well-being of all residents.
The allocation of police resources in a city with two neighborhoods - one rich and one poor - presents a challenging issue. In this scenario, both neighborhoods have the same population size, but different socio-economic characteristics. The rich neighborhood may have lower crime rates due to better security measures and access to resources, while the poor neighborhood may experience higher crime rates due to factors such as poverty, lack of education, and unemployment.
Given the budgetary restrictions, the city employs a police force of 20 officers. This raises the question of how to allocate these officers between the two neighborhoods to ensure the most effective use of resources.
One approach to this issue is to allocate officers based on crime rates. If the rich neighborhood has lower crime rates, then fewer officers can be assigned there, while more officers can be allocated to the poor neighborhood where crime rates are higher. This approach ensures that police resources are used where they are most needed.
Another approach is to allocate officers based on the severity of crimes. If the rich neighborhood has fewer but more severe crimes, then more officers may need to be assigned there to handle these cases. On the other hand, if the poor neighborhood has more but less severe crimes, then fewer officers may be required, but they may need to be more vigilant and proactive in preventing crime.
It is also important to consider community policing as a strategy to improve relationships between police officers and residents in both neighborhoods. By building trust and fostering communication, residents may be more willing to work with law enforcement to prevent crime and promote safety.
To learn more about police resources
https://brainly.com/question/30037107
#SPJ4
Complete question:
What does the variable c denote in a city with two neighborhoods - one rich and one poor - both with equal-sized populations, where the city employs a police force of 20 officers and p represents the number of police officers?
A) The number of police officers
B) The population of the rich neighborhood
C) The population of the poor neighborhood
D) The number of crimes.
Volume of this triangular prism
21 mm base
38 mm
82 mm long
28 mm
Answers
Answer:
43,624 mm cubed
Volume of Prisms Equation:
V=(Areabase)(height)
Volume of Triangular Prisms:
V=(1/2×base×height)(HEIGHT OF PRISM)
Step by Step Explanation:
V=(1/2×38×28)(82)
Cancelling:
cancel 2 and 28 making it 1 and 14
since the fraction is now 1/1 it is not needed
Back to Solving:
=38×14×82
=43,624 mm cubed
If kis a positive integer, find the radius of convergence of the series [infinity]∑n=0(n!)k(kn)!xn.
Answers
The given series is ∑(n!)(k^n)((kn)!)x^n. To find the radius of convergence, the radius of convergence for the given series is 0.
The given series is ∑(n!)(k^n)((kn)!)x^n. To find the radius of convergence, we can use the Ratio Test. The Ratio Test states that the radius of convergence R is given by:
R = 1/lim (n→∞) |(a_(n+1))/a_n|
where a_n represents the nth term of the series. For our series, a_n = (n!)(k^n)((kn)!)x^n. Let's find the ratio
|(a_(n+1))/a_n| = |[((n+1)!)(k^(n+1))((k(n+1))!)x^(n+1)]/[(n!)(k^n)((kn)!)x^n]|
Simplifying, we get
|(a_(n+1))/a_n| = |(n+1)(k)(((k(n+1))!))/((kn)!)x|
Now, let's take the limit as n approaches infinity:
lim (n→∞) |(n+1)(k)(((k(n+1))!))/((kn)!)x|
Since both the numerator and the denominator have factorials that grow rapidly, this limit is infinity. Therefore, the radius of convergence is:
R = 1/∞ = 0
So, the radius of convergence for the given series is 0.
To know more about integer visit :
https://brainly.com/question/1768254
#SPJ11
Determine which pair of functions are inverse functions. A. F(x) = x - 4
g(x) = x + 4
b. F(x) = x - 4
g(x) = 4x - 1
c. F(x) = x - 4
g(x) = (x - 4)/4
d. F(x) = 4x - 1
g(x) = 4x + 1
Answers
Since f(g(x)) = g(f(x)) = x, functions f(x) and g(x) are inverse functions.
The pair of functions in is inverse functions. A.
To determine whether two functions are inverse functions need to check if the composition of the two functions gives the identity function.
To check whether f(g(x)) = x and g(f(x)) = x.
Let's check each pair of functions:
f(x) = x - 4 and g(x) = x + 4
f(g(x)) = (x + 4) - 4
= x
g(f(x)) = (x - 4) + 4
= x
Since f(g(x)) = g(f(x)) = x, functions f(x) and g(x) are inverse functions.
f(x) = x - 4 and g(x) = 4x - 1
f(g(x)) = 4x - 1 - 4
= 4x - 5
g(f(x)) = 4(x - 4) - 1
= 4x - 17
Since f(g(x)) ≠ x and g(f(x)) ≠ x, functions f(x) and g(x) are not inverse functions.
f(x) = x - 4 and g(x) = (x - 4)/4
f(g(x)) = ((x - 4)/4) - 4
= (x - 20)/4
g(f(x)) = ((x - 4) - 4)/4
= (x - 8)/4
Since f(g(x)) ≠ x and g(f(x)) ≠ x, functions f(x) and g(x) are not inverse functions.
f(x) = 4x - 1 and g(x) = 4x + 1
f(g(x)) = 4(4x + 1) - 1
= 16x + 3
g(f(x)) = 4(4x - 1) + 1
= 16x - 3
Since f(g(x)) ≠ x and g(f(x)) ≠ x functions f(x) and g(x) are not inverse functions.
For similar questions on Inverse Function
https://brainly.com/question/3831584
#SPJ11
Jayla is the manager of Super Sandwiches. She recorded the number of sandwiches they sold each day during their Super Sandwich Sale.
Answers
The box plot that represents the data on the sandwiches sold by Super Sandwiches is Box Plot 1.
How to find the box plot ?The box plot that shows the data of sandwiches is the one that has the correct measure of the value of Q1 or the lower quartile. This is because the box plots are similar except for the lower quartile.
To find the lower quartile, arrange the numbers;
50, 66, 74, 88, 100, 109, 113, 127, 150
The lower quartile would be the median of the lower half of :
50, 66, 74, 88
The lower quartile is:
= ( 66 + 74 ) / 2
= 70
The first box plot has this Q1 value and so is correct.
Find out more on box plots at https://brainly.com/question/9827993
#SPJ1
The results of an awesome survey question are shown below.
If there were a popsicle stick for each selection, what is the probability of selecting one that says books without pictures, replacing it, and then selecting one that says audio books?
Round your answer to the nearest hundredth.
Answers
Answer:
Step-by-step explanation:
total number of sticks = 47+36+31= 114
Because you draw with replacement to find the probability of two events happening you simply just multiply them
p(books without pics) = #books without pics /#sticks
47/114 = 41.2280702%
p(audiobooks)= #audiobooks/ #sticks
31/114= 27.1929825%
p(books without pics and audiobooks)= p(books without pics) * p(audiobooks)
41.2280702%*27.1929825% = 11.21%
Investigate how the pattern progresses to the next terms 1,4,9,16
Answers
We can see that the pattern progresses by adding 3 to the previous perfect square to obtain the next term. The next few terms of the sequence would be:
25 (16 + 3)
36 (25 + 3)
49 (36 + 3)
64 (49 + 3)
81 (64 + 3)
...
We can continue this pattern to find as many terms as desired.
What is Number Sequences?
In mathematics, a number sequence is an ordered list of numbers that follow a specific pattern or rule. Each number in the sequence is called a term, and the position of a term in the sequence is called its index.
The given pattern appears to be a sequence of perfect squares starting from 1 and increasing by 3 at each step. We can verify this by observing that:
The first term is 1 which is a perfect square.
The second term is 4 which is a perfect square and is obtained by adding 3 to the previous term 1.
The third term is 9 which is a perfect square and is obtained by adding 3 to the previous term 4.
The fourth term is 16 which is a perfect square and is obtained by adding 3 to the previous term 9.
Therefore, we can see that the pattern progresses by adding 3 to the previous perfect square to obtain the next term. The next few terms of the sequence would be:
25 (16 + 3)
36 (25 + 3)
49 (36 + 3)
64 (49 + 3)
81 (64 + 3)
...
We can continue this pattern to find as many terms as desired.
To learn more about number sequence from the given link:
https://brainly.com/question/7043242
#SPJ4
find the gradient field of the function, f(x,y,z)=x2 4y2 4z2−1/2.
Answers
The gradient field of a function is a vector field that points in the direction of the maximum increase of the function. In the case of f(x,y,z) = x^2/4 + y^2/4 + z^2 - 1/2, the gradient field is given by <x/2, y, 2z>.
The gradient of a scalar field is a vector field that points in the direction of the maximum rate of increase of the scalar field, and its magnitude represents the rate of increase.
To find the gradient field of f(x,y,z), we first calculate the partial derivatives of f with respect to x, y, and z. The partial derivative of f with respect to x is 2x/4y2/4z2, the partial derivative of f with respect to y is -x2/2y3/4z2, and the partial derivative of f with respect to z is -x2/4y2/2z3/2. The gradient of f is then given by the vector field (2x/4y2/4z2)i - (x2/2y3/4z2)j - (x2/4y2/2z3/2)k, where i, j, and k are the unit vectors in the x, y, and z directions, respectively. This vector field represents the direction and magnitude of the maximum rate of increase of f at any point in space.
To learn more about vector fields click here: brainly.com/question/29815461
#SPJ11
which expression is equivalent to sin2β1 cosβ for all values of β for which sin2β1 cosβ is defined?
Answers
So, the equivalent expression for sin(2β) * cos(β) is 2sin(β)cos²(β) for all values of β where sin(2β) * cos(β) is defined.
We need to find an expression equivalent to sin(2β) * cos(β) for all values of β where it is defined. To do this, let's use the double-angle identity for sine.
The double-angle identity for sine states that sin(2α) = 2sin(α)cos(α). In our case, we have sin(2β) instead of sin(2α), so we can replace α with β in the identity:
sin(2β) = 2sin(β)cos(β)
Now, we can substitute this expression for sin(2β) into our original expression:
sin(2β) * cos(β) = (2sin(β)cos(β)) * cos(β)
Next, we need to simplify the expression by multiplying the terms:
2sin(β)cos²(β)
So, the equivalent expression for sin(2β) * cos(β) is 2sin(β)cos²(β) for all values of β where sin(2β) * cos(β) is defined.
To know more about equivalent expression visit:
https://brainly.com/question/28170201
#SPJ11
One of the first electronic computer was in the shape of a huge box it was 96 feet long and 2. 5feet wide the amount of the space inside was approximately 3000 cubic feet how many feet high was the computer
Answers
Hello! To find the height of the first electronic computer with the given dimensions and volume, we can use the formula for the volume of a rectangular prism:
Volume = Length × Width × Height
We are given the following dimensions:
Length = 96 feet
Width = 2.5 feet
Approximate Volume = 3000 cubic feet
Let's solve for the height:
3000 = 96 × 2.5 × Height
First, we will multiply the length and the width:
240 = 96 × 2.5
Now, divide both sides by 240 to find the height:
Height = 3000 / 240
Height ≈ 12.5 feet
So, the height of the computer was approximately 12.5 feet.
If you rolled two dice, what is the probability
that you would roll a sum of 10?
second
first
1 2 3 4
5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
6
Probability
Desired Outcome
All Outcomes
Simplify your fraction, then enter the numerator.
=
[?]
Enter
Answers
Answer:
Step-by-step explanation:
To calculate the probability of rolling a sum of 10 with two dice, we need to find the number of ways we can get a sum of 10 and divide that by the total number of possible outcomes. The sum of 10 can be obtained in three ways: (4, 6), (5, 5), and (6, 4). There are 36 possible outcomes when rolling two dice, since there are 6 possible outcomes for the first die and 6 possible outcomes for the second die. Therefore, the probability of rolling a sum of 10 is 3/36, which simplifies to 1/12.
The probability you will roll a sum of 10 is 1/12.
We have,
Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
To calculate the probability of rolling a sum of 10 with two dice, we need to find the number of ways we can get a sum of 10 and divide that by the total number of possible outcomes.
The sum of 10 can be obtained in three ways: (4, 6), (5, 5), and (6, 4).
The probability you will roll a sum of 10 = total times a sum of 10 is derived / total sample spaces
so, we get,
total times a sum of 10 is derived = (4 + 6) , (6 +4) , (5 + 5)
There are 36 possible outcomes when rolling two dice, since there are 6 possible outcomes for the first die and 6 possible outcomes for the second die.
Total sample spaces = 36
The probability you will roll a sum of 10 = 3/36 = 1/12
Therefore, the probability of rolling a sum of 10 is 3/36, which simplifies to 1/12.
To learn more on probability click:
brainly.com/question/11234923
#SPJ5
What are the exact side lengths of the triangle shown? Leave in radical form
Answers
Answer:
b = 4[tex]\sqrt{3}[/tex] , c = 8
Step-by-step explanation:
using the tangent and cosine ratios in the right triangle and the exact values
tan60° = [tex]\sqrt{3}[/tex] , cos60° = [tex]\frac{1}{2}[/tex] , then
tan60° = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{b}{4}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 4 )
b = 4[tex]\sqrt{3}[/tex]
then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{c}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
c = 4 × 2 = 8
if determining whether or not a measured effect can be distinguished from zero, we are interested in :a. practical significanceb. statistical significance
Answers
When determining whether or not a measured effect can be distinguished from zero, we are interested in statistical significance.
Statistical significance refers to the likelihood that the results of a study are not due to chance. In other words, it assesses whether the effect observed in a sample is likely to be a true effect in the population, or whether it could have occurred by chance. Statistical significance is typically assessed using hypothesis testing and a significance level (usually set at 0.05), which represents the probability of obtaining the observed results or more extreme results under the assumption that the null hypothesis (i.e., no effect) is true. If the probability is less than the significance level, the result is said to be statistically significant, indicating that the null hypothesis can be rejected and the observed effect is likely a true effect. Practical significance, on the other hand, refers to the importance or relevance of the observed effect in the context of the research question or real-world application.
Learn more about statistical significance here
https://brainly.com/question/15848236
#SPJ11
A 5 foot man is standing 8 foot away from a mirror. How far away is a 20 foot tree from the mirror?
Answers
The distance between the mirror and the 20-foot tree is 32 feet.
To solve this problemThe idea of comparable triangles can be used to calculate the separation between the mirror and the 20-foot tree.
Let's think about the triangles the man, the mirror, and the tree created. Similar triangles have comparable sides that are equal in ratio.
The dude is standing 8 feet away from the mirror and is 5 feet tall. As a result, we may establish the following ratio:
(Height of the man) / (Distance of the man from the mirror) = (Height of the tree) / (Distance of the tree from the mirror)
Substituting the known values:
5 / 8 = 20 / x
Where x represents the distance of the tree from the mirror.
Now, we can solve for x:
5x = 8 * 20
5x = 160
x = 160 / 5
x = 32
Therefore, the distance between the mirror and the 20-foot tree is 32 feet.
Learn more about ratio here : brainly.com/question/2328454
#SPJ1
Find the areas of the sectors formed by /DFE
Answers
The areas of the circular sectors are listed below:
Case 7: A = 50π / 3 in²
Case 8: A = 177.884 cm²
Case 9: A = 937.312 m²
Case 10: A = 10π / 3 ft²
How to find the area of a circular sector
In this problem we must determine the areas of four circular sectors, whose area formula is equal to:
A = (θ / 360°) · π · r²
Where:
θ - Measure of the central angle, in degrees.r - Radius.Now we proceed to determine the areas:
Case 7
A = (60 / 360) · π · (10 in)²
A = 50π / 3 in²
Case 8
A = (104 / 360) · π · (14 cm)²
A = 177.884 cm²
Case 9
A = (137 / 360) · π · (28 m)²
A = 937.312 m²
Case 10
A = (75 / 360) · π · (4 ft)²
A = 10π / 3 ft²
To learn more on areas of circular sectors: https://brainly.com/question/28804598
#SPJ1
because x-bar is an unbiased estimator of μ we know that:• sample averages have the same variance as the individual observations in the population. • values of the sample average are more Normal than individual observations. • values of sample averages are less variable than individual observations. • values of the sample average in repeated samples are not systematically too high or too low.
Answers
Because x-bar is an unbiased estimator of μ, sample averages have the same variance as the individual observations in the population.
The sample mean or x-bar is a statistic that estimates the population mean or μ. When we say that x-bar is an unbiased estimator of μ, it means that on average, the sample mean is equal to the population mean. This property is desirable because it means that our estimates are not systematically too high or too low.
One consequence of the x-bar being an unbiased estimator of μ is that sample averages have the same variance as the individual observations in the population. This means that the spread or variability of the sample mean is equal to the spread or variability of the individual observations. However, the central limit theorem tells us that the distribution of sample averages is more Normal than the distribution of individual observations. This is because as the sample size increases,
Learn more about unbiased estimator, here:
brainly.com/question/30237613
#SPJ11
HELP MEEEEEEEE PLEASE
Answers
The slope of the line that passes through the points ( -4,5) and (2,-3) is -4/3
What is slope of a line?The slope of a line is a measure of its steepness. It is also called gradient. It is the change in value on the vertical axis to the change in value on the horizontal axis.
Y axis is the vertical axis and x axis is the horizontal axis.
slope = [tex]y_2 -y_1)/x_2-x_1[/tex]
[tex]y_2[/tex] = -3
[tex]y_1[/tex]= 5x2 = 2x1 = -4
slope = -3-5/(2-(-4)
= -8/6
= -4/3
Therefore the slope of the line is -4/3
learn more about slope of line from
https://brainly.com/question/16949303
#SPJ1
Select all the numbers that are not written in standard form.
A
4.82
×
10
−
5
B
80
×
10
7
C
500
×
10
−
1
D
3.88
×
10
3
E
24
×
10
2
F
5
×
10
−
2
G
2.3
×
10
3
H
58.2
×
10
−
4
Answers
B
H
E
C
Standard form must be between 1 and 9
find an equation of the tangent plane to the surface at the given point. h(x, y) = ln x2 y2 , (3, 4, ln 5)
Answers
Step-by-step explanation:
To find the equation of the tangent plane to the surface at (3, 4, ln 5), we need to first find the partial derivatives of h with respect to x and y:
hx(x, y) = 2y^2/x
hy(x, y) = 2x^2/y
Then, we can plug in the point (3, 4) to get the partial derivatives evaluated at that point:
hx(3, 4) = 2(4^2)/3 = 32/3
hy(3, 4) = 2(3^2)/4 = 9/2
Now we can use the point-normal form of the equation of a plane, where the normal vector is given by ⟨hx(3, 4), hy(3, 4), -1⟩:
hx(3, 4)(x - 3) + hy(3, 4)(y - 4) - (z - ln 5) = 0
Substituting in the values for hx(3, 4) and hy(3, 4), we get:
(32/3)(x - 3) + (9/2)(y - 4) - (z - ln 5) = 0
Simplifying, we get:
(32/3)x + (9/2)y - z = 55/6
So the equation of the tangent plane to the surface at (3, 4, ln 5) is (32/3)x + (9/2)y - z = 55/6.
image...............
Answers
-2 is the equivalent average rate of change of f(x) with the interval.
Rate of change of a functionThe formula for calculating the rate of change of a function is expressed as:
[tex]f'(x) = \frac{f(b)-f(a)}{b-a}[/tex]
Given the function f(x) = 2x² + 12x + 16 with the interval [-3, -2]
f(-3) = 2(-3)² + 12(-3) + 16
f(-3) = 2(9) - 36 + 16
f(-3) = 18 - 20
f(-3) = -2
Similarly:
f(-2) = 2(-2)^2 + 12(-2) + 16
f(-2) = 2(4) - 24 + 16
f(-2) = 8 - 8
f(-2) = 0
Substitute the resulting values:
[tex]f'(x) = \frac{f(-3)-f(-2)}{-3-(-2)}\\f'(x)=\frac{-2-0}{-1}\\f'(x)=-2[/tex]
Hence the average rate of change of f(x) within the given interval is -2.
Learn more on average rate of change here: https://brainly.com/question/8728504
#SPJ1
A flare is launched from the deck of a lifeboat 4 ft above the water surface. The initial upward velocity is 80 ft/s. After how many seconds will the flare be 100 ft above the water surface?
Answers
Answer:
1.2 seconds
Step-by-step explanation:
100-4=96
96/80 = 1.2
Answer: 1 24/80 of a second
Step-by-step explanation:
Well so if you are at 4 ft after 1 second you need 16/80 of a second to reach 100 feet above because 80 then plus 16 plus the addition 4 ft that you are above the water would be 100 feet.
Help me with this pleaseeee i need it now help meeeeeee
Answers
Answer:
To test the null hypothesis that the mean mark is equal to 100 against the alternative that the mean mark is greater than 100, we can use a one-sample t-test since the population variance is unknown. Here's how you can perform the test:
Step 1: State the null and alternative hypotheses:
- Null hypothesis (H₀): The mean mark is equal to 100.
- Alternative hypothesis (H₁): The mean mark is greater than 100.
Step 2: Set the significance level (α):
In this case, the significance level is given as 0.05 or 5%.
Step 3: Compute the test statistic:
The test statistic for a one-sample t-test is calculated using the formula:
t = (X - μ) / (s / √n)
where X is the sample mean, μ is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.
Given:
X = 110 (sample mean)
s = 8 (sample standard deviation)
n = 13 (sample size)
μ (population mean under the null hypothesis) = 100
Substituting the values into the formula, we get:
t = (110 - 100) / (8 / √13)
t = 10 / (8 / √13)
t ≈ 3.012
Step 4: Determine the critical value:
Since the alternative hypothesis is one-tailed (greater than), we need to find the critical value for a one-tailed test at a 5% significance level with (n - 1) degrees of freedom. In this case, the degrees of freedom are 13 - 1 = 12.
Using a t-distribution table or statistical software, the critical value at α = 0.05 and 12 degrees of freedom is approximately 1.782.
Step 5: Make a decision:
If the test statistic t is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
In this case, the test statistic t is approximately 3.012, which is greater than the critical value of 1.782. Therefore, we reject the null hypothesis.
Step 6: State the conclusion:
Based on the sample data, there is sufficient evidence to support the claim that the mean mark is greater than 100.
Step-by-step explanation:
Use the graph of g(x) to answer the question.
The graph of g(x) is a translation of f(x)=x^2.
Write the equation for g(x) in vertex form
Answers
The equation for g(x) in vertex form is [tex]g(x) = ax^2[/tex], where "a" represents a constant that determines the shape and direction of the parabola.
The vertex form of a quadratic equation is given by:
[tex]g(x) = a(x - h)^2 + k[/tex]
where (h, k) represents the vertex of the parabola.
Since g(x) is a translation of [tex]f(x) = x^2[/tex], the vertex of g(x) will be the same as the vertex of f(x). The vertex of [tex]f(x) = x^2[/tex] is (0, 0).
So, the equation for g(x) in vertex form is:
[tex]g(x) = a(x - 0)^2 + 0\\g(x) = a(x^2)\\g(x) = ax^2[/tex]
Therefore, the equation for g(x) in vertex form is [tex]g(x) = ax^2[/tex], where "a" represents a constant that determines the shape and direction of the parabola.
Learn more about Parabola at:
https://brainly.com/question/29635857
#SPJ1
a rock is thrown from (2,1) to (12,18). how far did the rock travel
Answers
Answer:
18.136 units of distance
Step-by-step explanation:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) = (2, 1) and (x2, y2) = (12, 18)
d = sqrt((12 - 2)^2 + (18 - 1)^2)
= sqrt(10^2 + 17^2)
= sqrt(329)
≈ 18.136
Therefore, the rock traveled approximately 18.136 units of distance.
Does this graph show a function? Explain how you know.
-5
10
A. No; there are y-values that have more than one x-value.
B. Yes; there are no y-values that have more than one x-value.
C. No; the graph fails the vertical line test.
D. Yes; the graph passes the vertical line test.
Answers
The graph of y = -5x + 10 is a function because (d) yes, because it passes the vertical line test.
Checking if the relation y = -5x + 10 is a functionFrom the question, we have the following parameters that can be used in our computation:
y = -5x + 10
The above equation is a linear function
As a general rule of functions and relations
All linear functions are functions
This is because they pass the vertical line test
So, the true statement is (d)
Hence, the relation y = -5x + 10 is a function because (d) yes, because it passes the vertical line test.
Read more about vertical line test at
brainly.com/question/1821791
#SPJ1
Complete question
Does this graph show a function? Explain how you know.
y = -5x + 10
A. No; there are y-values that have more than one x-value.
B. Yes; there are no y-values that have more than one x-value.
C. No; the graph fails the vertical line test.
D. Yes; the graph passes the vertical line test.
please help i have no idea how to do this
Answers
The geometric sequence is -6, 1, -1/6, 1/36.......
Given is a geometric sequence, -6, ?, ?, 1/36 we need to find the missing terms,
So, we know that the ratios between the terms of a geometric sequence are common,
Let the 2nd term be x and the 3rd term be y, so,
-x/6 = 1/36 / y
-x/6 = 1/36y
6 = -36xy
x·y = -1/6
So, we get x·y = -1/6,
Now if we see the options, the third option gives 1 × -1/6 = -1/6,
Therefore, the terms can be written as,
-6, 1, -1/6, 1/36.......
If we see the common ratio we get,
-1/6
-1/6/1 = -1/6
1/36 / (-1/6) = -1/6
Hence the geometric sequence is -6, 1, -1/6, 1/36.......
Learn more about geometric sequence click;
https://brainly.com/question/13008517
#SPJ1
every matchbox manufactured by a certain factory contains no more than 20% defective matches. what is the minimum number of intact matches in a 43-match box manufactured by that factory?
Answers
If every matchbox contains no more than 20% defective matches, then at least 80% of the matches in a box must be intact. The minimum number of intact matches in a 43-match box manufactured by that factory is 34.
To find the minimum number of intact matches in a 43-match box, we need to multiply 43 by 80% (or 0.8):
43 x 0.8 = 34.4
Since we can't have a fraction of a match, we round down to the nearest whole number. Therefore, the minimum number of intact matches in a 43-match box manufactured by that factory is 34.
In a 43-match box manufactured by that factory, no more than 20% of the matches can be defective. To find the minimum number of intact matches, we can calculate the number of defective matches and subtract it from the total.
20% of 43 matches = (20/100) * 43 = 8.6
Since there can't be a fraction of a match, we round up to the nearest whole number, which is 9 defective matches. Now, subtract the number of defective matches from the total:
43 matches - 9 defective matches = 34 intact matches
The minimum number of intact matches in a 43-match box manufactured by that factory is 34.
learn more about defective here: https://brainly.com/question/14916815
#SPJ11
Information on a packet of seeds claims that the germination rate is 92%. In a packet of 160 seeds, 95% of the seeds germinated. What germination rate represents the 1^(st ) Quartile?
Answers
The 1st Quartile germination rate is 92%, the 1st Quartile germination rate represents the threshold below which 25% of the germination rates fall.
To determine this, we need to arrange the germination rates in ascending order and find the value that corresponds to the 25th percentile.
In this case, we have a packet of 160 seeds with 95% germination rate. To find the 1st Quartile germination rate, we need to consider the germination rates of the remaining 5% of seeds that did not germinate.
Since 92% is the claimed germination rate mentioned on the seed packet, we can assume that the 5% of seeds that did not germinate fall below this claimed rate. Therefore, the 1st Quartile germination rate is 92%.
The 1st Quartile, also known as the lower quartile or 25th percentile, divides a dataset into four equal parts. It represents the threshold below which 25% of the data points fall.
In this scenario, we have a packet of 160 seeds with a 95% germination rate. This means that 95% of the seeds successfully germinated. To find the 1st Quartile germination rate, we need to consider the remaining 5% of seeds that did not germinate.
Since the information on the seed packet claims a germination rate of 92%, we can assume that the 5% of seeds that did not germinate fall below this claimed rate.
As a result, the 1st Quartile germination rate is 92%. This indicates that 25% of the seeds in the packet had a germination rate below 92% while the remaining 75% had a germination rate equal to or higher than 92%.
To know more about rate click here
brainly.com/question/14018365
#SPJ11
the nurse manager of a rehab unit wants to purchase a new antiembolic stocking for the use with patients. To make a high-quality decision, the nurse manager would:
a. Involve the rehab staff in the decision.
b. Involve the sales representative.
c. Make the decision alone.
d. Involve administration in the decision.
Answers
A is wrong becuz the rehab staff don’t order medication they prescribe it
B is wrong becuz by involving a sales representative is like skipping administration and making the decision alone which make c also incorrect. ur welcome hopefully I’m right
Jacob is planning a garden. He has 12 fence posts and plans to place them 3 feet apart. How many feet of fence will this allow for the perimeter of the garden?
Answers
if Jacob wants to make a square or rectangular garden, each side can be up to 16.5 feet long, allowing for a total perimeter of 33 feet.
What is Perimeter?
Perimeter is the total distance around the edge of a two-dimensional shape, such as a polygon or a circle, and it is calculated by adding up the lengths of all of the sides of the shape.
A measuring cup is a kitchen tool used to measure the volume of liquid or bulk solid ingredients, typically made of glass or plastic and marked with graduated lines to indicate different measurements, such as milliliters, fluid ounces, and cups.
Jacob is planning a garden. He has 12 fence posts and plans to place them 3 feet apart. How many feet of fence will this allow for the perimeter of the garden?
If Jacob has 12 fence posts and plans to place them 3 feet apart, the perimeter of the garden will be 33 feet.
To see why, we can start with the fact that Jacob has 12 fence posts. Since he wants to place them 3 feet apart, we can imagine a straight line fence where each post is 3 feet away from the next one. The length of this line would be:
11 distances between posts x 3 feet per distance = 33 feet
However, a garden typically has four sides, so we need to divide this length by two to get the length of one side:
33 feet / 2 = 16.5 feet
Therefore, if Jacob wants to make a square or rectangular garden, each side can be up to 16.5 feet long, allowing for a total perimeter of 33 feet.
To know more about Perimeter visit:
https://brainly.com/question/397857
#SPJ4