Answers
Here, we are given a quadratic equation graph and we are tasked with getting the equation of the quadratic equation from the graph
The first thing we need to note here is the shape of the parabola.
This in the sense that if the parabola opens up or faces down
On the graph we can see that the parabola faces the positive x-direction
Generally, the equation of a quadratic graph is usually in the form below;
[tex]y=ax^2\text{ + bx + c}[/tex]So by identifying the values of a,b and c, we can get the complete equation of the graph
The above form is called the standard form while the form we have in the options is referred to as the vertex form
The vertex form can be written as;
[tex]y=a(x-h)^2\text{ + k}[/tex]Now, looking at the graph, we can see that the graph crosses the y-axis at the point y = 6
At this point, the value of x is 0
The vertex (h,k) represents the center point of the parabola
In the case of this question, the point is (-2,2)
so h =-2 and k is 2
What is left is to get a
we can obtain this from the value of y = 6 and x = 0
Thus;
6 = a(0-(-2))^2 + 2
6 = a(2)^2 + 2
6 = 4a + 2
4a = 6-2
4a = 4
a = 4/4 =1
So the equation in the vertex form is f(x) = (x + 2)^2 + 2
Related Questions
Which relation IS a function?
Answers
Answer: B.
Step-by-step explanation: A function relates an input to an output.
The relation which is a function is: function 1.
Option A is correct.
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).
A relation is a function when each input have only one output.
Function 1 have one output to each corresponding output.
Function 2 have two output for input x= 2.
Function 3 have two output for input x= 3.
Function 4 have two output for input x= 1.
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A used car dealership is interested in the age of a used car and the price of the vehicle. The manager collects a simple random sample of vehicles as shown in the table.
The equation of the least-squares regression line is
ŷ = 19.2 – 0.868x, where ŷ is the price of the vehicle (in thousands of dollars) and x is the age (in years). Which shows the residual plot?
ANSWER: A
Answers
Answer:
The Answer is A
Step-by-step explanation: Edge
the probability of a 4 child family having 4 girls is 0.5. is it true or false
Answers
Consider the phase space that consists of elements of the form (boy, boy, boy, boy), (girl, boy, boy, boy),...,(girl, girl, girl, girl).
There is a total of 2*2*2*2=2^4=16 possible combinations and each of them has the same probability to happen. Only one element is the case we are interested in (girl, girl, girl, girl).
Therefore, the probability of a family having 4 girls is
[tex]P(girl,girl,girl,girl)=\frac{1}{16}=0.0625[/tex]
The answer is false, the probability is 0.0625
I really need help with number 5
Answers
Given:
Required:
To find the distance from point B to line AC.
Explanation:
The point B touches the line AC at P.
And it is perpendicular.
The length of BP is 4.3.
Therefore, the distance from point B to line AC is 4.3.
Final Answer:
The distance from point B to line AC is 4.3.
8 - 5(3 + 2x)I need help
Answers
8 - 5(3 + 2x)
open the parenthesis
8 - 15 - 10x
-7 -10x
Find the 12th term in the arithmetic sequence an = 3 − 6(n − 1)a. -33b. -36c. -63d. -69
Answers
Given:
[tex]a_n=3-6(n-1)[/tex]Find-: 12th term of the sequence is
Sol:
[tex]\begin{gathered} a_n=3-6(n-1) \\ \end{gathered}[/tex]Where,
[tex]\begin{gathered} n=\text{ term.} \\ \\ n=12 \end{gathered}[/tex]Put the value then:
[tex]\begin{gathered} a_n=3-6(n-1) \\ \\ n=12 \\ \\ a_{12}=3-6(12-1) \\ \\ a_{12}=3-6(11) \\ \\ a_{12}=3-(6\times11) \\ \\ a_{12}=3-66 \\ \\ a_{12}=-63 \end{gathered}[/tex]So 12th term is -63
Answer:
-63
Step-by-step explanation:
How many graduates in the sample came from University A?
Answers
The number of graduates in the sample that came from University A is:
35 + 90 + 35 = 160 graduates
On average, Adrian's salary is 1.05 times the previous year's salary.If Adrian initially has $52,000 and n denotes the number of years, which recursive equation gives Adrian's annual income, /(7), as a function ofthe year?
Answers
Given:
Adrian initially has $52,000 and n denotes the number of years
Required:
Adrian's annual income, /(7), as a function of
the year?
Explanation:
Initially has $52,000, therefore
[tex]f(1)=52,000\text{ Exclude B,D}[/tex]The salary is 1.05 times the previous year's salary.
[tex]f(n)=1.05.f(n-1),\text{ for n}\ge2[/tex]Required answer:
Option D
solve for the following right triangle upper a and h
Answers
we have that
[tex]undefined[/tex]Write an equation to represent , the balance in an account after years, with an initial investment of $1,000 with an interest rate of 3%, compounded each year.
Answers
The balance in the account after years of compound interest arrangement can be represented by the equation; Balance = 1,000 (1.03)^n.
Which equation represents the balance in the account after years of compound interest?It follows from the task content that the equation which represents the balance in the account after years is required to be determined.
It follows that the principal amount is; $1,000 while the interest rate is; 3%.
This indicates that after each year, the new balance is 103% of the preceding balance.
Hence, the exponential equation which correctly represents the balance at any point in time is;
Balance = 1,000 (1.03)^n.
Where n = number of years after.
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Find the perimeter and area of
the figure if each unit on the
graph measures 1 centimeter.
Round answers to the nearest
tenth, if necessary.
A(2, 1)
B(8, 6).
C(10, 1)
Answers
The figure's perimeter and area would be as follows.
Perimeter = 21.19 cm
Area = 25.501 cm²
What is coordinate system?A Cartesian coordinate system in some kind of a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular lines that are aligned to the point and are both measured in the same length.
According to the given data:point of the coordinates are as follows:
A(2, 1)
B(8, 6).
C(10, 1)
We know that the formula for finding for the distance is:
d=√((x2 – x1)² + (y2 – y1)²).
For Point AB:
X₁ = 2
Y₁ = 1
X₂ = 8
Y₂ = 6
putting the values onto formula we get:
d=√((x2 – x1)² + (y2 – y1)²).
d=√((8 – 2)² + (6 – 1)²).
d=√((6)² + (5)²).
d=√(36 + 25).
d=√(61).
AB =7.81
For Point BC:
X₁ = 8
Y₁ = 6
X₂ = 10
Y₂ = 1
putting the values onto formula we get:
d=√((x2 – x1)² + (y2 – y1)²).
d=√((10 – 8)² + (1 – 6)²).
d=√((2)² + (-5)²).
d=√(4 + 25).
d=√(29).
BC = 5.38
For Point CA:
X₁ = 10
Y₁ = 1
X₂ = 2
Y₂ = 1
putting the values onto formula we get:
d=√((x2 – x1)² + (y2 – y1)²).
d=√((2 – 10)² + (1 – 1)²).
d=√((-8)² + (0)²).
d=√(64 + 0).
CA = 8
The perimeter of the given figure is:
Sum of all the sides.
AB + BC + CA
7.81 + 5.38 + 8
21.19 cm
Now finding the area of the tringle we use Pythagoras formula:
H² = P² + B²
P² = H² - B²
P² = (7.81)² - (5.38)²
P = 9.4837
We know that the area of the triangle is: = 1/2(base * Hight).
= 1/2(5.38 * 9.48)
= 25.501 cm²
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A cooking for the nursing home is preparing 100 yeast rolls for dinner the dry ingredients needed include 14 1/8 cups of flour 6 3/8 cups of sugar and 3/8 cups of salt how many cups of dry ingredients are in this recipe
Answers
Given the following ingredients
Cups of flour = 14 1/8 = 113/8 cups
Cups of sugar = 6 3/8 cups = 51/8 cups
Cups of salts = 3/8 cups
Calculate the total cups of dry ingredients
[tex]Total\text{ cups}=\frac{113}{8}+\frac{51}{8}+\frac{3}{8}[/tex]Find the LCM
[tex]\begin{gathered} Total\text{ cups}=\frac{113+51+3}{8} \\ Total\text{ cups}=\frac{167}{8} \\ Total\text{ cups}=20\frac{7}{8}cups \\ Total\text{ cups}=19+1\frac{7}{8} \\ Total\text{ cups}=19+\frac{15}{8} \\ Total\text{ cups}=19\frac{15}{8}cups \end{gathered}[/tex]Therefore there are 19 15/8 cups of dry ingredients in this recipe
Does our data provide enough evidence to prove that New York police are racially biased (in terms of use of force)? Why or why not?
Answers
We want to proof for this case if there is enough evidence to conclude that the New York police are racially biased in terms of force
From the info given is possible to see that the proportion with High level of force used is higher for Black people compared to White people. A difference of 6.3-5.8% = 0.5%.
In the other hand, we can see that for the Hands up force level, there is a significant difference between the two proportions, higher for Black compared to White with a difference of 15.1-9.7%= 5.4%
And finally when we analyze the case for No force used, we can see that there is a higher percentage for White (84.4%) compared to Black (78.7%) with a difference of 5.7%.
Based on this results we can conclude that in general the New York police is partially biased since is possible to see that for any level of force used the records are in favor of the White people.
18 is how many times more then 6
Answers
Answer: 3 times more
Step-by-step explanation:
what is the reciprocal for the fraction 5/7 ?
Answers
we know that
The reciprocal of a number is: 1 divided by the number
If you multiply a number by the reciprocal, the result is 1
so
we have
5/7
so
the reciprocal is 7/5
Verify
(5/7)(7/5)=1 -----> is ok
PLEASE SOLVE THIS IM GIVING 40 POINTS
Answers
The coordinates of the point P lying between AB is found as (7, -2/5).
What is termed as the section formula?The Section formula is used to calculate the coordinates of a point that separates a line segment either internally or externally into a certain ratio. When a point separates a line segment in some ratio, we just use section formula to determine the coordinates of the that point.For the given question;
The two end coordinates are;
(x₁, y₁) = (8, 0)
(x₂, y₂) = (3, -2)
The ratio of the division is;
AP/PB = 1/4
OR
m:n = 1:4
The Formula for finding the coordinates of P for internally crossing is;
x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Put the values;
x = (mx₂ + nx₁)/(m + n)
x = (1×3 + 4×8)/(1 + 4)
x = (3 + 32)/5
x = 7
Now for y coordinates.
y = (my₂ + ny₁)/(m + n)
y = (1×(-2) + 4×0)/(1 + 4)
y = -2/5
Thus, the coordinates of the point P lying between AB is found as (7, -2/5).
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Fin tends to exaggerate. He says if he stacked all the quarters he's ever spent on gumball machines, they would reach to the moon. The distance to the moon is about [tex]3.85 \times {10}^{8} [/tex]m and the width of a quarter is about[tex]1.75 \times {10}^{ - 3} [/tex]m. If Fin's claim were true, how many quarters has he spent on gumball machines?
Answers
For this problem we were given the distance to the moon and the width of a quarter in meters. We need to determine how many quarters we would need to stack in order to reach the moon.
In order to solve this problem, we need to divide the distance from the surface of the Earth to the moon by the width of each quarter. Notice that both numbers are presented in scientific notations, therefore we need to divide the coefficients and subtract the exponents. This is done below:
[tex]\begin{gathered} n=\frac{3.85\cdot10^8}{1.75\cdot10^{-3}} \\ n=2.2\cdot10^{8-(-3)} \\ n=2.2\cdot10^{8+3} \\ b=2.2\cdot10^{11} \end{gathered}[/tex]If Fin's claim were true, he'd need to stack a total of 2.2*10^11 quarters.
Jordan looks at the line plot. He says the difference between the most capacity and the least capacity is 1/4 gallon. He says he knows the difference without subtracting. Explain Jordan’s mistake and find actual difference between measurements.
Answers
In a line plot the maximum value is the rightmost mark in the line plot; in this case the maximum capacity is 2 1/2. On the other hand the minimum value is the leftmost mark in the line plot, here the minimum is 1 1/2. Let's calculate the difference between them:
[tex]2\frac{1}{2}-1\frac{1}{2}=1[/tex]Therefore, the difference between the maxiimum and minimum capacity is 1.
1) Consider the ratio table below that compare hours worked to money earned for an employee at a pizza restaurant. Hours Worked 4 12 16 ? Money Earned 36 ? 76 108 144 270 a. How much money would an employee earn for working 8 hours? b. How many hours did a person work if they earned $270? c. Find the ratio associated with the table above (in simplest form). d. If you extend the ratio table, how much money will be earned if an employee works 24 hours? dollars they can amount of time
Answers
The ratio table can be used to find the amount earned and the number of hours worked based on the ratio of the values as follows;
a. A person that works for 8 hours earns $72
b. A person that earns $270 worked for 30 hours
c. The ratio is 9 : 1
d. The earnings of a person that works for 24 hours is $216
What is a ratio table?A ratio table is one that shows the constant relationship between the value pairs on the table.
The given ratio table is presented as follows;
Hours Worked; 4, 12, 16, ?
Money Earned; 36, 108, 144,
Required;
a. The amount a person will earn if he or she works for 8 hours
Solution;
Let x represent the hours worked, and let y represent the money earned
y = k•x
Therefore;
k = y/x
From the ratio table, we have;
k = 36/4 = 108/12 = 144/16 = 9
k = 9
y = 9•x
The amount earned, y for working 8 hours, x is therefore;
y = 9 × 8 = 72
The amount earned for working 8 hours is $72
b. The number of hours worked if a person earns $270
If a person earned $270, we have;
270 = 9 × x
x = 270/9 = 30
The number of hours worked if a person earned $270 is 30 hours
c. The ratio associated with the table in the simplest form is 36 : 4 = 9 : 1
d. The amount earned if a person worked 24 hours
Solution;
y = 9•x
Which gives;
y = 9 × 24 = 216
The amount earned if a person worked 24 hours is $216
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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.3 years, and standard deviation of 1.1 years.If you randomly purchase one item, what is the probability it will last longer than 10 years?Use the normal table and round answer to four decimal places
Answers
We want to find the following probability:
[tex]P(X>10)[/tex]where X is a normal random variable with mean 13.3 and standard deviation 1.1. To find this probability let's normalize the random variable; to do this we use the z-score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Then, in this case, we have:
[tex]P(X>10)=P(z>\frac{10-13.3}{1.1})=P(z>-3)[/tex]Using the standard normal table, we have:
[tex]P(X\gt10)=P(z\gt(10-13.3)\/1.1)=P(z\gt-3)=0.9987[/tex]Therefore, the probability of purchasing an item with a lifespan greater than 10 years is 0.9987
What is the measure
Answers
Here, we want to get the measure of the angle marked A
We are going to use the sides given
The trigonometric ratio that links the adjacent to the hypotenuse is the cosine
The cosine is the ratio of the adjacent to the hypotenuse
Mathematically;
[tex]\begin{gathered} \cos \text{ m}\angle CAB\text{ = }\frac{12}{15} \\ \\ m\angle CAB\text{ = }\cos ^{-1}(\frac{12}{15}) \\ \\ m\angle CAB\text{ = 36.87} \end{gathered}[/tex]Write two numbers that multiply to the value on top and add to the value on bottom.
Answers
The values are -3 and -26
What is Multiplication?
A product is an expression that identifies the object to be multiplied, called the result of a multiplication, or coefficient. For example, 30 is the product of 6 and 5, and x\cdot is the product of x.
We have to find the number which is multiply to give the upper value and sum up to give the bottom value
So, the value of these numbers will be
-3 x -23 = 69
-3 + (-23) = -26
Hence the values are -3 and -23
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Complete the vertical algorithm to evaluate the product.Please see image below
Answers
Solution
Complete the vertical algorithm to evaluate the product:
Therefore the product of the expression is
[tex]4.09656[/tex]10) Given that a=4 b=2 and C=-1
find the value of:
1) a - b + c
11) 20
Answers
Answer:
1 is the answer
Step-by-step explanation:
a-b+c Substitute values into the equation
4-2+(-1)
2+(-1)
2-1
1 Answer
The value of: 1) a - b + c is, 1 is the solution.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
a=4 b=2 and C=-1
now,
a-b+c
Substitute values into the equation
we get,
4-2+(-1)
=2+(-1)
=2-1
=1 (Answer)
Hence, The value of: 1) a - b + c is, 1 is the solution.
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The temperature in the morning was –2º F. The temperature in the evening was 9º F higher than it was in the morning. What was the temperature in the evening?
Answers
Answer:
Step-by-step explanation:
-2f
Can someone help with 16,17 and 18 ! thank you !
Answers
In questions 16, 17 and 18 we have a right triangle and in the three cases you know the measues for 2 sides, except for hipotenuse.
We can use the following relation to solve the problem:
[tex]tg(x)=\frac{\text{Opposite side}}{Adjacent\text{ side}}[/tex]16)
[tex]\begin{gathered} tg(x)=\frac{\text{1}7}{7}=2.4285 \\ tg(x)=2.4285 \\ x=tg^{-1}(2.4285) \\ x=68\degree \end{gathered}[/tex]17)
[tex]\begin{gathered} tg(x)=\frac{8}{10}=0.8 \\ x=tg^{-1}(0.8) \\ x=39\degree \end{gathered}[/tex]18)
[tex]\begin{gathered} tg(x)=\frac{\text{1}1}{8}=1.375 \\ x=tg^{-1}(1.375) \\ x=54\degree \end{gathered}[/tex]what is the answer of this problem ? help me to find
Answers
Given:
Total invested amount = $9000
One account = 5%
Another account = 6%
Find-:
Invested amount of each equation
Explanation-:
Let in 5% account invested amount is x
then amount in 6% account is (9000-x)
Then,
[tex]5\%\text{ of }x+6\%\text{ of }(9000-x)=510[/tex]Then the value of "x" is:
[tex]\begin{gathered} \frac{5}{100}\times x+\frac{6}{100}\times(9000-x)=510 \\ \\ 0.05x+0.06(9000-x)=510 \\ \\ 0.05x+(0.06\times9000)-0.06x=510 \end{gathered}[/tex]The "x" is:
[tex]\begin{gathered} 0.05x-0.06x+540=510 \\ \\ -0.01x=510-540 \\ \\ -0.01x=-30 \\ \\ x=\frac{-30}{-0.01} \\ \\ x=3000 \end{gathered}[/tex]The value of x is 3000 the mean amount in 5% invested amount is 3000.
6% invested amount is:
[tex]\begin{gathered} =9000-3000 \\ \\ =6000 \end{gathered}[/tex]So each account invested amount is:
[tex]\begin{gathered} 5\%\rightarrow3000 \\ \\ 6\%\rightarrow6000 \end{gathered}[/tex]Can Some one please help me match the congruence statements below!
Answers
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 70
grams of an alloy that contains 12% copper with 90 grams of pure copper.
(a) How many grams of copper are in the resulting mixture?
(b) What percentage of the resulting mixture is copper?
Answers
a)There is 160 grams of copper are in the resulting mixture
b) There is 61.5% percentage of the resulting mixture is copper.
What are mathematics operations?
• An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.
• The operation's arity is determined by the number of operands.
• Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.
• A zero-arity operation, also known as a nullary operation, is a constant.
• The mixed product is an example of an arity 3 operation, also known as a ternary operation
From the question:
a) Suppose that a certain alloy is made by mixing 70 grams of an alloy that contains 12% copper with 90 grams of pure copper.
The number of grams of copper in the resulting mixture = 70 grams + 90 grams = 160 grams
b) 70 grams of an alloy that contains 12% copper = 70 × 12%
= 70 grams × 0.12
= 8.4 grams
The number of grams of copper in the resulting mixture = 160 grams
The percentage of the resulting mixture that is copper is
=( 8.4 grams + 90 grams of pure copper/160) × 100
= 98.4/160 × 100
= 61.5%
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CRITICAL THINKING Find the values of a, b, and c so that the linear system shown has (---1. 2. --3) as its only solution. Explain your reasoning. x + 2y - Bra -r-y +z = b 2x + 3y - 2z=c enter your answer as follows: a=_,b=_,c=__without any spaces. Show Your Work
Answers
1) Let's set the system of linear equations:
x +2y -3z = a
-x -y +z = b
2x +3y -2z =c
2) Since the solution has already been given ( -1,2,-3) all that's left to do, is to plug it into each equation so that we can find a, b and c. Just like this:
x +2y - 3z = a ⇒ (-1) +2(2) -3(-3) = a ∴ a = 4
-x -y +z = b ⇒ -(-1) -(2) +(-3) = b ∴ b = 0
2x +3y -2z =c ⇒ 2(-1) +3(2) -2 (-3)=c ∴ c = -2
3) Hence, a = 4 b = 0 and c = -2