The vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
The given quadratic function is f(x) = 2(x - 3)² + 4.
We need to find the key features of the given quadratic function.
What is the quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
Now, the key features of the given quadratic function as follows:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (3, 4)
Focus: (3, 33/8)
Axis of Symmetry: x=3
Directrix: y=31/8
Plot these points (1, 12), (2, 6), (3, 4), (4, 6) and (5, 12) on the graph.
Therefore, the vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
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find the three postive consecutive integers such that the product of the smallest and the largest is 17 more than 3 times the median intger
Answer:
find the three postive consecutive integers such that the product of the smallest and the largest is 17 more than 3 times the median intger
Answer: 5, 6, 7
Step-by-step explanation:
Let three positive consecutive integers equal to x, x+1, x+2
Hence,
[tex]\displaystyle\\x(x+2)-3(x+1)=17\\x^2+2x-3x-3=17\\x^2-x-3-17=17-17\\x^2-x-20=0\\x^2-5x+4x-20=0\\x(x-5)+4(x-5)=0\\(x-5)(x+4)=0\\x-5=0\\x-5+5=0+5\\x=5\in\ (x > 0)\\x+4=0\\x+4-4=0-4\\x=-4\notin\ (x > 0)\\5+1=6\\5+2=7[/tex]
PLEASE HELP ME ANSWER 34,36
-2+(-3)+(-4)+(-5)+(-6)+(-7)
Answer:
-27
here is the answer for you
Which expression is equivalent to √125x6^y15^z3^?
Answer:
[tex]5x^2y^5z[/tex]
Step-by-step explanation:
Hello!
Expand the cube root:
[tex]\sqrt[3]{125x^6y^{15}z^3}[/tex][tex]\sqrt[3]{125}* \sqrt[3]{x^6} * \sqrt[3]{y^{15}}*\sqrt[3]{z^3}[/tex]Use exponent rule:
[tex]\sqrt[a]{b^c} = b^{\frac ca}[/tex]Simplify[tex]\sqrt[3]{125}* \sqrt[3]{x^6} * \sqrt[3]{y^{15}}*\sqrt[3]{z^3}[/tex][tex]5^{\frac33}*x^{\frac63}*y^{\frac{15}{3}}*z^{\frac33}[/tex][tex]5 * x^2 * y^5 * z[/tex][tex]5x^2y^5z[/tex]The answer is [tex]5x^2y^5z[/tex].
17+|-12--5|--16
show how you got the answer
To estimate the percent of red marbles in a large bag of marbles, margo will use the following sampling method. She will randomly select a marble, record its color, put it back into the bag, shake the bag to thoroughly mix the marbles, and then repeat those steps. She will perform the procedure many times. What type of sampling method is margo using?.
It is found that Margo are going to be using sampling.
• sampling in statistics may be a a part of the sampling technique within which each sample has an equal probability of being chosen. In other words, a sample chosen randomly is an unbiased representation of the entire population.
Sample strategies is also classified as :
1) Convenient: The sample that is taken from a pool that is readily accessible.
2) Random : When all options are into a hat and draw a number of team
3) Systematic : Every kth element
4) Cluster : once we divide population into groups called clusters, and every element of cluster is surveyed.
5) Stratified : In stratified also divides the population into groups, However just some of the weather of the group are surveyed. per the question Marbles are taken from the bag, and after they're taken they're again placed back within the bag so it depicts sampling.
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Each time John rides the bus to school he pays $3. Write and solve an equation that represents the change in John's money from riding the bus to and from school for 17 days
Every day that John rides on the bus, he loses $3
if he rides on the bus for 17 days, it can be solved like this
(3 x 2)17 = 102$
The change is John's money is -$102 over a span of 17 days
Hope this helped
A rectangle restaurant kitchen has a perimeter of 38 m in an area of 88 m² what are the dimensions of the kitchen
The dimensions of the kitchen are 11m × 8m.
In geometrical mathematics, a polygon with four sides is referred to as a quadrilateral, while a quadrilateral with two opposed, parallel, and equal sides is referred to as a rectangle.
A rectangle has four equal-sized angles. There are four angles in a rectangle.
A rectangle has 90° angles on all sides.
The rectangle's diagonal is the separation or length of a line segment that connects any two opposed vertices.
Let l and w represent the length and breadth of the rectangular kitchen, respectively.
we know that area of a rectangle = length × width
perimeter of a rectangle = 2(l ₊ b)
Given that the rectangular kitchen has an area of 88 m².
A = 88 m²
l × w = 88 m² ....eq(1)
The perimeter of the rectangle is 38 m.
Perimeter (P) = 38 m
2(l+w) = 38 m
l+w = 19 m
l = 19 - w .....eq(2)
substitute eq(2) in eq(1).
l × w = 88 m²
(19 - w)w = 88
19w - w² = 88
-w²+19w-88 = 0
w²-19w+88 = 0
By factorization method, we get:
w²-11w-8w+88 = 0
w(w-11)-8(w-11) = 0
(w-11)(w-8)
w = 11 or w = 8
If w = 11,
then l = 19-11 = 8m
and If w = 8m
then, l = 19-8 = 11m
so the dimensions are 11m×8m
Hence we get the dimensions of the kitchen are: 11m×8m
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Linear distribute properties 6(y+3)=30
Answer:
y=2
Step-by-step explanation:
6 times y and six times 3
6y+18=30
-18 -18
6y=12
divide both sides by 6 and you will get y=2
Find q in this equation
17. The difference of a number and 12 is three. Find the number.
A polynomial p(x) is given as 2x^2-3kx+5
One of the zeros of p(x) is -1
Find k.
Answer:
[tex]k = -\frac{7}{3}[/tex]
Step-by-step explanation:
Given :
p(x) = 2x² − 3kx + 5
Since, -1 is a zero for p then :
p(-1) = 0
Solving the equation p(-1) = 0 for k :
p(-1) = 0
⇔ 2(-1)² − 3k(-1) + 5 = 0
⇔ 2 + 3k + 5 = 0
⇔ 3k = -5 - 2
⇔ 3k = -7
⇔ k = -7/3
NOTE :
If -1 is a zero of p
[tex]\Longrightarrow k = -\frac{7}{3}[/tex]
[tex]\Longrightarrow p(x) = 2x^2 - 3(\frac{-7}{3}) x + 5\\\Longrightarrow p(x) = 2x^2+ 7x + 5[/tex]
Bacterial Growth Exponential Function
Bacterial growth is expressed by an exponential function with the formula of [bacteria]=ae^[time]b
need help asap WILL GIVE YOU BRAINLIEST
Thanks!!!
Answer:
14 is an obtuse angle
Step-by-step explanation:
An obtuse angle is an angle that is bigger than 90° degrees but doesn’t reach a straight line at 180°.
Rachel received a 90$ gift card for a coffee store
That's great for Rachel! I would love a gift card as well where is this at?
What is 32 Quartz to 48 Quartz?
32 Quartz to 48 Quartz is 2/3 Quartz
What is Quart measurement ?The quart is a measurement which is use to find the capacity of liquid. Or we can say Quart is a unit of liquid volume which is measured in gallon. There are different measurements into which we can convert the unit such as ounces and liters. These conversion values are as below :
Mathematically, we can write :
In terms of ounces1 quart = 32 fluid ounces
In terms of liters1 quart = 0.94 US liters = 4 cups (approx.)
According to given question, 32 Quartz to 48 Quartz is the ratio of 32 and 48 Quartz value.
Mathematically, we can write :
[tex]\frac{32 \ Quartz }{48 \ Quartz}\\ \\= \frac{2 \ Quartz}{3 \ Quartz} \\\\or, = \frac{2}{3} Quartz[/tex]
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What is a function and how can I identify one ?
Answer:
a function is a rule or correspondence by which each element x is associated with a unique element y.
hope this was helpful!
The following table shows the different savings account available at Capital Bank. Use the table to answer questions
Kate is depositing $5,000 into an account for her son’s education. Which account should she choose?
A. Teen Savings, because her son is a teen
B. College Savings, because she meets the minimum deposit and it earns more interest
C. Regular Savings, because it earns compound interest.
D. Platinum Savings, because it has the highest interest rate.
Based on the accounts and the benefits they offer, Kate should choose B. College Savings, because she meets the minimum deposit and it earns more interest
Which account is best for Kate?Kate should pick the college savings account for two reasons with the first being that the $5,000 she wants to deposit meets the minimum deposit amount of $1,000.
The second reason is that the account earns more interest than other account.
Even though it is simple interest, the 9% is still much higher than the compound interest of 1% that the regular account gives.
Kate should choose college savings.
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A six-sided dice is rolled twice. The sides are labeled 1-6. What
is the probability of rolling an odd number and then rolling a 2?
(Give your answer as a reduced fraction).
A 3/36
B 1/18
C 1/12
D 1/36
The probability of rolling an odd number and then rolling a 2 is 1/12.
Option C is true.
What is Probability?
Probability is measure of the likelihood of an event to occur.
Given that;
A six - sided dice is rolled twice.
The sides are labelled 1-6.
Now,
In a dice odd number are 1, 3, 5
Hence, The probability of rolling an odd number = 3/6
And, The probability of rolling a 2 = 1/6
So, The probability of rolling an odd number and then rolling a 2
= 3/6 x 1/6
= 1/12
Hence, The probability of rolling an odd number and then rolling a 2 is 1/12.
Option C is true.
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Exercise
Respond to the following based on your reading.
1. Which numbers are to the right of 0 on the number line?
2. Which numbers are to the left of 0 on the number line?
3. Is 0 an integer?
4. Draw a number line with integers from –3 to 6.
5. Solve the problems:
a. −8 + 0 =
b. 1 × (−14) =
c. 19 ÷ 1 =
d. 0 × 104 =
e. −21 − 0 =
Answer:
please solve this question 4²×3³×(-1)¹²²
the density of a certain material is such that it weighs 3 grams per fluid ounce of volume. express this density in ounces per liter. round your answer to the nearest hundredth.
The density in ounces per liter is 3.57826 rounding off = 3.58
Density of a substance can be defined as a relationship between the mass and the volume of that substance.
[tex]Density=\frac{Mass}{Volume}[/tex]
For Example if a metal have a mass 0f 7gm and volume as [tex]5cm^{3}[/tex]
[tex]Density=\frac{7}{5} = 1.4g/cm^{3}[/tex]
we know that 1 gram/fluid ounce of volume = 1.19275 ounces/liter
1 gm/fluid ounce =1.19275 ounces/liter
3 gm/fluid ounce = 3*1.19275 ounces/liter
So 3 gm/fluid ounce = 3.57826 ounces/liter
On rounding it to nearest hundredth we get 3.58 ounces/liter
Therefore the density of the material which weighs 3 gm/fluid ounce in ounces/liter is 3.58.
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Simplify as far as possible.
2√3+3√3
Answer: 0.51639777..
Step-by-step explanation:
3/v=8/13 using cross prouducts property
Answer:
v = 4.875
Step-by-step explanation:
Anytime you have a proportion (a fraction = a fraction)
you can cross multiply to change the equation (get rid of the fractions!) and solve.
see image.
3/v = 8/13
8v = 39
v = 4.375
see image.
The length of a rectangular sign is 3 feet longer than the
width. If the sign's area is 54 square feet, find its length and
width.
(Anyone else taking Algebra 2?)
Answer:
length is 9 and width is 6
Step-by-step explanation:
List the factors of 54 and choose the numbers that only have a difference of 3. In this case it is 6 and 9, then put them in the order they go based on the instructions.
What is the natural number of the square root of 8
One freezer costs $623.95 and uses 90 kilowatt hours (kwh) of electricity each month. A second freezer costs $500 and uses 100 kwh of electricity each month. The expected life of each freezer is 12 years. What is the minimum electric rate in cents per kwh for which the 12-year total cost (purchase price + electricity costs) will be less for the first freezer?
The minimum electric rate in cents per kwh for which the 12-year total cost will be less for the first freezer is 8.61 cents
How to calculate the rate?Let x = minimum electric rate (Cents/kWh)
Total months in 12 years is 12*12 = 144 m
1st freezer
Total cost over 12 years is
623.95 (cost) + (90 kWh/m)*(144 m)(x/100 $/kWh)
= 623.95 + 129.6x
2nd freezer
Total cost over 12 years is
500 + 100*144*(x/100)
= 500 + 144x
For the 1st freezer to cost less over 12 years,
623.95 + 129.6x < 500 + 144x
123.95 < 14.4x
8.61 < x
The minimum rate is 8.61 cents per kWh
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Is 10 squared greater than or less then or equal to 5
Answer:
10 squared is 100 so 10 squared is greater than 5.
Step-by-step explanation:
Hope its corrects and it helps you!
I WILL GIVE 35 POINTS TO THOSE WHO ANSWER THIS PROBLEM RIGHT NOOOO SCAMS
Using translation concepts, we have that:
4. The type is f(x + k), with k = 3, and a horizontal shift.
5. The type is kf(x), with k = 5 and a vertical stretch.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For graph 4, we have function g(x) is a shift left of 3 units of function f(x), hence:
The type is f(x + k), with k = 3, and a horizontal shift.
For graph 5, we have that for each value of x, g(x) = 5f(x), hence:
The type is kf(x), with k = 5 and a vertical stretch.
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A
C
3.
Find m2LMN if mLME=24°
and mLEMN = 42°
66⁰
18⁰
M
B
D
24⁰
42⁰
Answer:
this question is impossible!11!1!!!!
Step-by-step explanation:
none
find the angle measure then classify the angle (I'm very bad at this one and I need help instantly
Answer:
30,70,110
Step-by-step explanation:
12. acute
13. acute
14. obtuse