Answers
We are given the following function
\(f(x)=-x^2+2x-2\)The standard form of a quadratic function is given by
\(f(x)=ax^2+bx+c\)Comparing the given function with the standard form, we see that
a = -1
b = 2
c = -2
It is usually preferred to write the function in vertex form for graphing
The vertex form is given by
\(f(x)=a(x-h)^2+k\)Where h is the vertex (maximum/minimum point of the graph) and is given by
\(h=-\frac{b}{2a}=-\frac{2}{2(-1)}=-\frac{2}{-2}=1\)Where k is given by
\(\begin{gathered} k=f(h) \\ k=f(1) \\ k=-(1)^2+2(1)-2 \\ k=-1+2-2 \\ k=-1 \end{gathered}\)So, we have
a = -1
h= 1
k = -1
Therefore, the vertex form of the given function is
\(\begin{gathered} f(x)=a(x-h)^2+k \\ f(x)=-(x-1)^2-1 \end{gathered}\)Related Questions
Hallie collects beanbag animals. She
started her collection eight weeks ago
with six animals. Each week since then,
she has been given two more animals.
How many beanbag animals does she
have now? Please help meeee
Answers
Answer:
can i see a ss of the question?
Step-by-step explanation:
I need help pls I need to get to 80%
Answers
Answer:
False (no)
Step-by-step explanation:
A polygon needs at least three straight sides and angles
7. A sixth-grade class has 12 boys and 8 girls.
The teacher wants to divide them into
groups that have the same number of boys
and the same number of girls. What is the
greatest possible number of groups the
teacher can make?
A. 4 groups
C. 6 groups
D. 2 groups
B. 8 groups
Answers
Graph the point on the graph.
Answers
Answer:
see below
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph
Answer:
Info down in Explaination
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.07 and the probability that the flight will be delayed is 0.18. The probability that it will not rain and the flight will leave on time is 0.8. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.
Answers
The probability that it is raining if the flight has been delayed is 0.07, or 7%.
How to calculate the probabilityWe can use the following formula to calculate the probability that it is raining if the flight has been delayed:
P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)
We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):
= 0.07 * 0.18
= 0.0126.
Substituting these values into the formula, we get:
P(Rain|Delayed) = 0.0126 / 0.18 = 0.07
Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.
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2p + 7p = 54
Need to share more work
Answers
Answer:
p=6
Step-by-step explanation:
2p + 7p = 54
Combine like terms
9p = 54
Divide by 9
9p/9 = 54/9
p = 6
Answer:
p=6
Step-by-step explanation:
We are given the equation:
\(2p+7p=54\)
We want to find p, so we must isolate p on one side of the equation.
First, combine like terms on the left side of the equation. Both terms have the variable "p" and can be added.
\((2p+7p)=54\)
\(9p=54\)
p is being multiplied by 9. The inverse of multiplication is division. Divide both sides of the equation by 9.
\(\frac{9p}{9}=\frac{54}{9}\)
\(p=\frac{54}{9}\)
\(p=6\)
Let's check our solution. Plug 6 in for p and solve.
\(2p+7p=54\)
\(2(6)+7(6)=54\)
\(12+42=54\)
\(54=54\)
This checks out, so we know our solution is correct.
The solution is 2p+7p=54 is p=6
In Bridget's class, 35% of the students chose pizza as their favorite food. If 14 of the students chose pizza as their favorite food, how many students are in the class?
Answers
Answer:
40 students are in the class :)
Step-by-step explanation:
35%=14
1%=14/35=0.4
0.4*100=40=100%
Point A is plotted on the coordinate plane below. Determine the location of Point C given the following criteria: Point C has integer coordinates. The graph of line AC is not a function.
Answers
ANSWER
\((3,4)\)EXPLANATION
We want to find the location of point C such that C has integer coordinates and the graph of line AC is not a function.
For the graph of line AC not to be a function, it implies that the graph of line AC must be perpendicular to the x-axis. In other words, the graph of line AC must be a vertical line.
This, therefore, implies that point C can lie anywhere on the vertical line that passes through point A. In other words, it will have the same x-coordinate as A but a different integer y-coordinate.
The coordinates of A are (3, 2). Hence, we can pick the location of point C to be:
\(C(3,4)\)That is the answer.
Which inequality has the solution shown below?
0.3x+8 <3
0.2x+5>2
←++
-18 -17 -16 -15 -14 -13 -12
0.4x +7<1
0.52+6>3
Answers
social health is one component of the health tringal what are the other two components
Answers
Answer:
mental health and emotional health
Find the measure of the arc or angle indicated.
Answers
The measure of the arc or angle is:
m∠NLM = 60 deg
How to find the measure of the arc or angle indicated?From the given figure, line LN is the diameter. Thus, the measure of arc LN is 180° (semicircle).
Thus, we can say:
arc NM + arc ML = 180°
(3x + 21) + (8x + 16) = 180°
11x + 37 = 180
11x = 180 - 37
11x = 143
x = 143/11
x = 13
arc NM = 8x + 16
put x = 13:
arc NM = 8(13) + 16 = 120°
Recall that:
The measure of inscribed angle is half the measure of its intercepted arc. That is:
m∠NLM = 1/2 * 120°
m∠NLM = 60°
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what is inequalities
Answers
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.
The most common symbols used in inequalities are:
">" (greater than): indicates that the value on the left side is larger than the value on the right side.
"<" (less than): indicates that the value on the left side is smaller than the value on the right side.
"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.
"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.
"≠" (not equal to): indicates that the values on both sides are not equal.
Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
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A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1080 feet of fencing material, what should be the length and width of the field?
Answers
The width of the field is 230 feet and the length is 310 feet.
Let's denote the width of the field as "x" feet.
The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.
To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:
2(length) + 2(width) = perimeter
Substituting the given values:
2(x + 80) + 2(x) = 1080
2x + 160 + 2x = 1080
4x + 160 = 1080
4x = 920
x = 920/4
x = 230
Therefore, the width of the field is 230 feet.
Now we can find the length by adding 80 feet to the width:
Length = Width + 80 = 230 + 80 = 310 feet.
So, the width of the field is 230 feet and the length is 310 feet.
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Which fraction is equivalent to -1/6?
Answers
Answer:
1/-6
Step-by-step explanation:
Determine if the point (4, -3) is a solution
to the following system:
x - y = 4.
2x + y = 5
Determine if the point (4,-3) is a solution
Answers
A movie theater charges $8.50 for an adult ticket to an evening showing of a popular movie. To help the local animal shelter, the theater management has agreed to reduce the price of each adult ticket by $0.50 for every can of pet food a customer contributes to a collection barrel in the theater lobby. Which of the following shows both an equation in which y represents the cost of an adult ticket in dollars for a customer who contributes x cans of pet food, and the graph of the cost if a customer brings in 2, 5, 8, or 10 cans of pet food?
Answers
Answer: What’s the answer ?
Step-by-step explanation:
A card is drawn at random from a standard pack of playing cards.
Then a fair coin is flipped.
What is the probability of selecting a Queen and the coin landing on tails?
Answers
If a card is drawn at random from a standard pack of playing cards.The probability of selecting a Queen and the coin landing on tails is: 1/26.
What is probability?Probability can be defined as the tendency or likelihood that an event will occur.
Hence,
Let P(queen) be:
P(queen) = 4/52 = 1/13
Let P(tails) = 1/2
So the probability of selecting a Queen and the coin landing on tails is:
P(queen and tails) = (1/13)× (1/2)
P(queen and tails) = 1/26
Therefore the P(queen and tails) is 1/26.
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Dont put the file stuff like stop! Help me
Mrs. Davis has 5/4 lb of dry dog food. She will put an equal
amount of food into 3 containers. How much dog foor will
be in each container?
Answers
This seems like a division problem so you would take (5/4) and divide it by 3 to make 3 equal groups meaning 5/12lb would be in each container.
I hope this helps, good luck!
Pls tell the value of Y pls pls
Answers
4 × y - y = 36
4y - y = 36
Combining 4y and -y to get 3y
3y = 36
Dividing both sides by 3
y = 36/3
y = 12.
\(4 \times y - y = 36 \\ = > 4y - y = 36 \\ = > 3y = 36 \\ = > y = \frac{36}{3} \\ = > y = 12\)
The answer is 12.ANSWER ASAPPPP PLS
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2
3
4
5
6
Answers
Answer:
I'm going to help you figure this out because I am actually on the same assignment. If you do not understand what it is asking, it is not asking you to break down the function notation, it is simply asking you to substitute (X) with 2,3,4,5,and 6 and then to solve it on each line
The circumference of a circle is 15pi centimeters what is the area of the circle in terms of pi?
Answers
\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)
According to Wikipedia, the following are the lengths of terms of the US Presidents that preceded Joe Biden. There is a total of 44. You may have expected to see a total of 45, as Biden is the 46th us President, but Grover Cleveland was considered the 22nd and the 24th President, but is only counted once in this list The 2922 is the length of two full terms and the 1461 is the length of one full term FDR, the 4422 in the table, had actually started his FOURTH term before dying in office The 31 is William Henry Harrison who became ill shortly after his inauguration. His death may have been due to pneumonia Number of US Presidents 12 1 1 Term in Days 4422 2922 2865 2.840 2.728 2.041 2.027 1.886 1,654 1.503 1,461 1.460 1.430 1.419 1 1 12 1 1 1.419 1.262 1,036 969 895 881 492 199 31 TOTAL: 1 1 1 1 1 1 1 1 1 44 Determine the mean, median and mode for this set of data Give each to the nearest whole day Mean = Median = Mode = and With one of the modes being a high value as well as the term of FDR being much higher than all others, was pulled up to a higher value than another of hte measures of central tendency the
Answers
The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.
To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:
Mean:
To find the mean, we add up all of the term lengths and divide by the total number of terms:
Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44
Mean = 1743.77 days
Median:
To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:
31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422
Median = (1460 + 1461) / 2
Median = 1460.5 days
Mode:
The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.
Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.
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The electrical resistance varies directly as the square of the voltage (V
) and inversely as the electric power (P
). If the voltage is 20
volts and the electric power is 5
watts, then the electrical resistance is 80
ohms.
Answers
The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.
The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.
In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.
The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.
According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms
Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.
Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.
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The graph shows a proportional relationship, y = kx
HURRY ASAPPPPP
What is the constant of proportionality, k?
Answers
Answer:
if you pay attention when x = 1 y=4 and when x=2 y=8, then the proportionality constant is equal to 4
Step-by-step explanation:
Can some one please explain how to do this? 1.253 x 7.4 =
Answers
Answer:
9.2722
Step-by-step explanation:
7.400
*1.252
_____
9.2722
Its simple, plz rate 5 str, thx, and brailiest
Jeremy determines that √9= 9^1/2. Part of his work is shown
√9=3=3^1=3^1/2 + ^1/2=____=9^1/2
Which expression or equation should be placed in the blank to correctly complete Jeremy's work?
A: (3^2)^1
B: 3^1/2 + 3^1/2
C: 3^1/2 x 3^1/2= (3x3)^1/2
D: 3^1/2 x 3^1/2= (3x3)^1/2+^1/2
Answers
Equation (A) 3¹ can be placed correctly in Jeremy's work.
What are equations?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.So, in the given situation Jeremy determines that: \(\sqrt{9}=9^{\frac{1}{2}}\)
Which is obtained by the working: \(\sqrt{9}=3=3^1=3^{\frac{1}{2}+\frac{1}{2}}=3^1=9^{\frac{1}{2}}\)The part that is missing: \(\frac{1}{2}+\frac{1}{2}=1\)If two halves equal a whole, the answer is 3¹.Therefore, the equation that should be placed correctly in Jeremy's work is (A) 3¹.
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The complete question is given below:
Jeremy determines that √9= 9^1/2. Part of his work is shown
√9=3=3^1=3^1/2 + ^1/2=____=9^1/2
Which expression or equation should be placed in the blank to correctly complete Jeremy's work?
A: 3¹
B: (3^2)^1
C: 3^1/2 + 3^1/2
D: 3^1/2 x 3^1/2= (3x3)^1/2
E: 3^1/2 x 3^1/2= (3x3)^1/2+^1/2
he owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on weekdays and weekends. The owner samples 5 weekdays and finds an average of 259.23 gallons of milk sold on those days with a standard deviation of 34.713. 10 (total) Saturdays and Sundays are sampled and the average number of gallons sold is 365.12 with a standard deviation of 48.297. Construct a 90% confidence interval to estimate the difference of (average number of gallons sold on weekdays - average number of gallons sold on weekends). Assume the population standard deviations are the same for both weekdays and weekends.
Answers
Answer:
90% confidence interval is ( -149.114, -62.666 )
Step-by-step explanation:
Given the data in the question;
Sample 1 Sample 2
x"₁ = 259.23 x"₂ = 365.12
s₁ = 34.713 s₂ = 48.297
n₁ = 5 n₂ = 10
With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }
significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1
Since we are to assume that variance are equal and they are know, we will use pooled variance;
Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13
Now, pooled estimate of variance will be;
\(S_p^2\) = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]
we substitute
\(S_p^2\) = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]
\(S_p^2\) = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [ 4 + 9 ]
\(S_p^2\) = [ 4819.9692 + 20993.4 ] / [ 13 ]
\(S_p^2\) = 25813.3692 / 13
\(S_p^2\) = 1985.64378
Now the Standard Error will be;
\(S_{x1-x2\) = √[ ( \(S_p^2\) / n₁ ) + ( \(S_p^2\) / n₂ ) ]
we substitute
\(S_{x1-x2\) = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]
\(S_{x1-x2\) = √[ 397.128756 + 198.564378 ]
\(S_{x1-x2\) = √595.693134
\(S_{x1-x2\) = 24.4068
Critical Value = \(t_{\frac{\alpha }{2}, df\) = \(t_{0.05, df=13\) = 1.771 { t-table }
So,
Margin of Error E = \(t_{\frac{\alpha }{2}, df\) × [ ( \(S_p^2\) / n₁ ) + ( \(S_p^2\) / n₂ ) ]
we substitute
Margin of Error E = 1.771 × 24.4068
Margin of Error E = 43.224
Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89
So, Limits of 90% CI will be; x₁ - x₂ ± E
Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114
Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666
Therefore, 90% confidence interval is ( -149.114, -62.666 )
Whats the answer to it i can't figure it out
Answers
Answer:
-0.1
...............................
-0.1
Step-by-step explanation:
-1/7 = -0.142857
-0.1 = -0.10
-0.1 > -1/7
Translate the word phrase into a math expression.
1 less than a number.
n + 1
1−n
15 ÷ n
n−1
ACK ACK I NEED HELP PLZZ im dummmmm
Answers
N-1
Hey there!
The answer is n - 1.
Let's pretend the number is 15, so 1 less than "15", if you think about it, would be 14, and to get there, you do 15 - 1, now let us switch "15" back to a number "n", and now we have "n - 1"
Did you catch on? ;)
I would love to help you anytime
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 5 or 8? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
ANSWER
The probability of getting a sum of 5 or 8 is 1/4
STEP-BY-STEP EXPLANATION
