Answer: The value of 'h' is 3.
Step-by-step explanation: Given that the vertex form of a function is given by
[tex]g(x)=a(x-h)^2+k~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the value of 'h' when the following function is converted to the vertex form.
[tex]g(x)=x^2-6x+14~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (ii), we have
[tex]g(x)=x^2-6x+14\\\\\Rightarrow g(x)=x^2-2\times x\times 3+3^2-3^2+14\\\\\Rightarrow g(x)=(x-3)^2-9+14\\\\\Rightarrow G(x)=(x-3)^2+5.[/tex]
Comparing it with the vertex form (i), we get
[tex]h=3.[/tex]
Thus, the value of 'h' is 3.
The value of h in the vertex form is -3.
How to find the value of h?
in the vertex form:
g(x)=a(x−h)^2 + k
h is the x-value of the vertex.
Remember that for the general quadratic equation:
y = a*x^2 + b*x + c
The vertex is at:
h = -b/2a
So in our equation:
g(x) = x^2 - 6x + 14
We will have:
h = -(-6)/2*1 = 3
h = 3
That is the value of h.
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Derek wrote the following paragraph proof for the Vertical Angles Theorem:
The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 by the transitive property of equality. Angle 1 is equal to angle 3 _____________________.
Which phrase completes the proof?
by construction using a straightedge
by the definition of a perpendicular bisector
by the subtraction property of equality
by the vertical angles theorem
subtraction property of equality (i just took that test and got it right)
Sue’s Corner Market has a markup of 60% on bottled water. If the market sells a bottle of water for $2, find the original amount that Sue pays.
Markup is the amount added to the cost price of goods to cover overhead and profit.
Sue’s Corner Market has a markup of 60% on bottled water.
Let us say original price was $x.
Now price after markup is $2.
So we can make an equation like:
original price + markup price = price after markup
x + 60% of x =2
[tex] x + 0.6x =2 [/tex]
[tex] 1.6x =2 [/tex]
dividing both sides by 1.6
x= 1.25
So original price was 1.25 dollars.
Answer:
1.25 dollars.
Step-by-step explanation:
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Each trip, a bus drops off more fans at a concert. On the first trip, the bus dropped off 30. On the 14th trip, which was the last one, the bus dropped off 95 fans. How many fans did the bus deliver to the concert in total
Answer: There are 875 fans the bus deliver to the concert in total.
Step-by-step explanation:
Since we have given that
On the first trip, the bus dropped off = 30
Here a = first term = 30
On the 14 trip, the last trip, the bus dropped off = 95
i.e. [tex]a_{14}=95[/tex]
So, the total number of fans the bus deliver to the concert is given by
[tex]S_{14}=\frac{n}{2}(a+a_n)\\\\S_{14}=\frac{14}{2}(30+95)\\\\S_{14}=7(30+95)\\\\S_{14}=125\times 7\\\\S_{14}=875[/tex]
Hence, there are 875 fans the bus deliver to the concert in total.
At combs store there is a 25% chance a customer enters the store within one minute of closing time. Describe the complementary event and find its probability
Carla sells hot coffee, cider and tea from a sidewalk cart near wall street in new york city. last month she sold $4,500 worth of product to 1,000 customers. she spent $800 on buying her beverages in bulk. her monthly costs are: utilities = $100, salary = $2,000, advertising = $0, insurance = $0, interest = $0, rent (cart) = $600, depreciation = $0. calculate carla's average sale per customer.
The average sale per customer for Carla is $4.50.
To find Carla's average sale per customer, we need to determine the total revenue and the total number of customers.
The average sale per customer is calculated by dividing the total revenue by the total number of customers.
Given:
- Total revenue for the month: $4,500
- Total number of customers for the month: 1,000
The average sale per customer is calculated as:
[tex]\[ \text{Average sale per customer} = \frac{{\text{Total revenue}}}{{\text{Total number of customers}}}. \][/tex]
Plugging in the given values:
[tex]\[ \text{Average sale per customer} = \frac{{4,500}}{{1,000}} = 4.5. \][/tex]
Thus, the average sale per customer for Carla is $4.50.
Question :
Carla sells hot coffee, cider and tea from a sidewalk cart near wall street in new york city. last month she sold $4,500 worth of product to 1,000 customers. she spent $800 on buying her beverages in bulk. her monthly costs are: utilities = $100, salary = $2,000, advertising = $0, insurance = $0, interest = $0, rent (cart) = $600, depreciation = $0. calculate carla's average sale per customer.
What is the median of this data set?
The median of a data set with an even number of values is calculated by taking the average of the two middle values. For a data set with an odd number of values, the median is simply the middle value.
Explanation:The median of a data set with an even number of values is calculated by taking the average of the two middle values. For example, if the data set is 6.8, 7.2, the median would be (6.8 + 7.2) / 2 = 7.
However, if the data set has an odd number of values, the median would simply be the middle value. For example, if the data set is 3, 5, 8, the median is 5.
It's important to note that the median is used to find the middle value of a data set and is often preferred over the mean when there are outliers in the data.
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Find the area of a circle with a circumference of \color{blue}{6\pi}6πstart color blue, 6, pi, end color blue.
Find the product. (2 p + 7)(3 p - 9)
6 p^2 - 3 p - 63
6 p^2 + 3 p - 63
6 p^2 + 39 p - 63
6 p^2 + 3 p - 2
You are driving at an average speed of 50 miles per hour. You drive 22 hours, and you still need to drive another 175 miles. Which graph models how far you are from your destination at any point in time?
How can you check to see if two ratios form a proportion? Explain the method you used to find the answer to the previous problem.
Answer:
Write a proportion using the ratios. Find the cross products. If the cross products are equal, then the ratios form a proportion.
Step-by-step explanation:
Amy has 12 pairs of white socks, 2 pairs of gray socks, and 6 pairs of black socks in her drawer. if she takes two pairs without replacement, what is the probability that she will take a white pair and gray pair?
A used book store buys a hardback book for $1.50 and then sells it for $5. Over time, the store sells the same number of books it buys. The store manager can use the equation P(x)=5x−1.5x to determine the store's profit, P(x), where x is the number of books that the store sells. Which statement about the book store is true based on the profit equation?
A.The book store makes a profit of $5.00 for each hardback book that is sold.
B.The book store makes a profit of $3.50 for each hardback book that is sold.
C.The book store makes a profit of $4.50 for each hardback book that is sold.
D.The book store sells each hardback book for $3.50
A used book store buys a hardback book for $1.50 and then sells it for $5. Over time, the store sells the same number of books it buys. The store manager can use the equation P(x)=5x−1.5x to determine the store's profit, P(x), where x is the number of books that the store sells. Which statement about the book store is true based on the profit equation?
Cost Price of book, C.P.=$1.50
Selling Price of book, S.P.=$5
PROFIT=S.P. -C.P.
So, Profit=$5-$1.50=$3.50
So, Profit=$3.50 on each book
Or, we are given P(x)= 5x-1.50x
Or, P(x)=3.50x
For each book, we must divide the profit P(x) by x, that is, number of books
[tex] \frac{P(x)}{x}=\frac{3.5x}{x} [/tex]
[tex] \frac{P(x)}{x}=\frac{3.5*1}{1} [/tex]
[tex] \frac{P(x)}{x}=3.5 [/tex]
So, Profit for each book sold is $3.50
Answer:Option C
Answer:
C
Step-by-step explanation:
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I have a Brainliest reward
A right triangle has a leg of 13 cm and a hypotenuse of 21 cm. What is the length of the other leg? Round to the nearest tenth
A. 8.0 cm
B.16.5 cm
C. 24.7 cm
D. 272.0 cm
The other leg of the right triangle will be 16.5cm.
Legs of a right triangle:The side which shares the common/neighboring border to the right angle in a triangle is called legs.
Pythagoras theorem:It states that the sum of the areas of the two squares on the legs equals the area of the of the square on the hypotenuse.
According to the given question, we have
length of one leg of the right triangle is 13cm.
hypotenuse of the right triangle is 21 cm .
Let x be the length of the other leg.
Now, according to the Pythagoras theorem
We can write as
[tex](21)^{2} = x^{2} +(13)^{2}[/tex]
⇒ 441 = [tex]x^{2} +169[/tex]
⇒[tex]441-169 =x^{2}[/tex]
⇒ [tex]272 =x^{2}[/tex]
⇒ [tex]x = \sqrt{272}[/tex]
⇒[tex]x = 16.49[/tex] ≈ 16.5cm
Hence, the other leg of the right triangle will be 16.5cm.
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What is the surface area of the cone to the nearest whole number ? Use 3.14 for π
Answer:
1130.973355 is the answer
Step-by-step explanation:
pi10(10+sqrrt((24^2)+(10^2)))
31.416(10+sqrrt(576+100))
31.416(10+sqrrt(676))
31.416(10+26)
31.416(36)
1130.976
A boat in calm seas travels in a straight line and ends the trip 16 km west and 50 km north of its original position. Find the direction of the trip to the nearest tenth of a degree.
Uli wants to write the phrase “the difference of seven and a number squared” as an algebraic expression. She wrote out several expressions in the table. Which expression correctly represents the phrase?
Answer:
The Algebraic expression that correctly represents the phrase 'the difference between 7 and a number squared' is
= 7 - x²
Step-by-step explanation:
Let's represent the unknown number be represented as x
The unknown number is also squared = x²
Therefore, the Algebraic Equation correctly representing the phrase 'difference of 7 and a number squared' is
= 7 - x²
Oliver and Peter had the
same length of string. Oliver used 3
4 of
his string to tie a bundle of newspapers.
Peter used 6
8 of his string to tie a bundle
of magazines. Who used more string?
Draw a number line and write a
comparison to show your answer
Answer:
Oliver and Peter both uses same length string.
Explanation:
Suppose length of rope or string = x meters
Oliver divide his rope into four equal parts
[tex] \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4} [/tex]
Each part length is [tex] \frac{1}{4} [/tex]
NOw Oliver used 3 part of the string out of four parts
that means total used string is 3/4
Now peter also have same length of string = x meter
He divides the string eight equal parts and use the 6 parts out of 8
each part length is :[tex] \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} [/tex]
Use 6x/8
simplify the fraction 6x/8
divide by 2 both numerator and denominator
6x/8 = 3x / 4
So both uses same part of string.
Type the correct answer in each box. If necessary, use / for the fraction bar(s). Richard has 3 times as many music CDs as Benny does. If Richard has y CDs, the number of CDs Benny has is given by the expression . If Richard has 30 CDs, Benny has CDs.
Answer:
[tex]y=3x[/tex]
when Richard has 30 CDs, Benny has 10 CDs.
Step-by-step explanation:
Richard has 3 times as many music CDs as Benny does.
Let Benny has 'x' CD's.
If Richard has 'y' CDs, the number of CDs Benny has is given by the expression :
[tex]y=3x[/tex]
If Richard has 30 CDs, means y = 30
So, x will be => [tex]30=3x[/tex]
[tex]x=30/3=10[/tex]
So, when Richard has 30 CDs, Benny has 10 CDs.
help !! Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1?
a (1, –1)
b (0, 0) and (0, –1)
c (0, 0) and (2, 0)
d no solutions
I need help ASAP! will give Brainliest!
It's geomtery
Look at the picture below // 99 points // PLEASEE HELPP
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Old macdonald had a total of 37 chickens and pigs on this farm. there was a total of 98 feet. how many chickens were there and how many pigs?
The required, there were 25 chickens and 12 pigs on Old MacDonald's farm.
To solve this problem, we can use a system of equations to represent the number of chickens and pigs on Old MacDonald's farm. Let x be the number of chickens and y be the number of pigs. Then we have:
x + y = 37 (equation 1)
2x + 4y = 98 (equation 2)
Equation 1 represents the total number of animals, and Equation 2 represents the total number of legs. We can simplify equation 2 by dividing both sides by 2:
x + 2y = 49 (equation 3)
Now we have two equations with two variables. We can solve for x and y by using substitution or elimination. Let's use elimination by multiplying equation 1 by 2 and subtracting it from equation 3:
x + 2y = 49
-2x - 2y = -74
x = -25
Solving for x, we get:
x = 25
Substituting x = 25 into equation 1, we get:
25 + y = 37
Solving for y, we get:
y = 12
Therefore, there were 25 chickens and 12 pigs on Old MacDonald's farm.
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The equations are c + p = 37 and 2c + 4p = 98. Solving the system of equations the numbers are 26 and 11, respectively.
Explanation:To solve this problem, we can use a system of equations.
Let's assume that the number of chickens is represented by 'c' and the number of pigs is represented by 'p'. Based on the given information, we can create two equations:
1. c + p = 37 (equation 1)
2. 2c + 4p = 98 (equation 2)
We have two equations with two variables, so we can solve this system of equations to find the values of 'c' and 'p'.
Using equation 1, we can express 'c' in terms of 'p': c = 37 - p.
Substituting this into equation 2, we get: 2(37 - p) + 4p = 98. Solving this equation, we find: p = 11.
Substituting the value of 'p' back into equation 1, we find: c = 26.
Therefore, Old MacDonald had 26 chickens and 11 pigs on his farm.
Use the parabola tool to graph the quadratic function f(x)=−5x2−2.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
[tex] \text{Consider the quadratic function}\\ \\ f(x)=-5x^2-2\\ \\ \text{For a quadratic equation, }f(x)=ax^2+bx+c, \text{ we know that the x-coordinate}\\ \text{of the vertex (h,k) is given by}\\ \\ h=\frac{-b}{2a}\\ \\ \text{on comparing the given equation with standard equation, we have} [/tex]
[tex] a=-5, b=0, c=-2\\ \\ \text{so the x-coordinate of the vertex is }\\ \\ h=-\frac{b}{2a}=-\frac{0}{2(-5)}=0\\ \\ \text{so plug this vlaue of the h in the given function to get the y-coordinate}\\ \text{of the vertex. so}\\ \\ f(x)=-5(0)^2-2=0-2=-2\\ \\ \text{hence the vertex of the parabola is: }(h,k)=(0,\ -2)\\ \\ \text{A second point on the graph can be found by putting x=1, so }\\ \\ f(1)=-5(1)^2-2=-5-2=-7\\ \\ \text{so one other point on the parabola is }(1,-7) [/tex]
The grpah of the quadratic function is shown below:
Answer:(0,-2) (1,-7)
Step-by-step explanation:
help:/
Determine if the number is written in scientific notation. If not explain.
1. 4.8x100^7
No; it is not written as a number times a power of 10
yes; the number is written in scienfic notation
no; the first factor is not a number between 1 and 10
2. 5.1x10^-8
yes; the number is written in scienfic notation
no; the first factor is not a number between 1 and 10
no; it is not written as a number times a power of 10
I need help with this equation! Carbon-14 has a half-life of 5730 years. Derek has a sample of a fossil that has 33mg of its original 100 mg of carbon-14. Find the decay constant, k, and use it to answer the questions that follow.
First use the formula P(t)=Ae ^{kt} , to find the decay constant, k
What does (r−c)(3) mean about George's new store?
subtract r from c to get 8x+10
replace x with 3
8(3) +10 = 34 which in hundreds is 3400 dollars
the answer is C
Anybody got an answer?