Use the Parabola tool to graph the quadratic function.
f(x)=3x^2−6x+5
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answers
graphed below:
[tex]\sf f(x)=3x^2-6x+5[/tex]
vertex: (1, 2)cuts y-axis: (0, 5)
Answer:
Given function: [tex]f(x)=3x^2-6x+5[/tex]
Vertex form: [tex]y=a(x-h)^2+k[/tex]
(where [tex](h, k)[/tex] is the vertex)
Expand vertex form:
[tex]y=ax^2-2ahx+ah^2+k[/tex]
Compare coefficients of given function with expanded vertex form
Comparing coefficient of [tex]x^2[/tex]:
[tex]3=a[/tex]
Comparing coefficient of [tex]x[/tex]:
[tex]\ \ \ \ \ -6=-2ah\\\implies-6=-2 \cdot 3h\\\implies -6=-6h\\\implies h=1[/tex]
Comparing constant:
[tex]\ \ \ \ \ \ 5=ah^2+k\\\implies5=3(1)^2+k \\\implies 5=3+k\\\implies k=2[/tex]
Therefore, the vertex is (1, 2)
As the leading coefficient is positive, the parabola will open upwards.
Additional plot points:
[tex]f(0)=3(0)^2-6(0)+5=5[/tex]
[tex]f(2)=3(2)^2-6(2)+5=5[/tex]
(0, 5) and (2, 5)
Related Questions
Can someone help me please
Answers
Both lines would be the same length.
4x-6 = 50
Add 6 to both sides:
4x = 56
Divide both sides by 4:
x = 14
How many degrees are in 25π18?
Answers
Answer:
[tex]\displaystyle 250°[/tex]
Explanation:
When converting from radians to degrees, multiply one hundred eighty by the radian measure, then divide it pi:
[tex]\displaystyle \boxed{250°} = 1\frac{7}{18}\pi[\frac{180}{\pi}][/tex]
I am joyous to assist you at any time.
Helppp Please!!!!!!!!
Answers
Answer:
Emma began her journey at 7:30 a.m., at 8 a.m. she was 20 miles away, she stayed for an hour and a half, she left at 10 a.m., she was 7.5 miles from her house at 11:45, she traveled 80 miles total
Step-by-step explanation:
please let me know what you don't understand here. because this is really simple.
the distance from home is increasing and then decreasing when she is traveling.
the rate of distance per time would give us even the speed with which she was traveling.
when there is no change in the distance over time, that means she was "stationary" - either at home or at her grandmother's place.
so, let's answer the questions :
(a)
movement started at 7:30am (that is when she began her journey).
(b)
20 miles
you pick 8am on the time scale and move straight up until you hit the curve. and then you check what value is at that point all the way to the left on the distance scale : 20.
(c)
from 8:30am to 10am = 1.5 hours.
we see this by the interval on the time scale for which the curve is totally flat (a horizontal line) = no change in distance from home during that time.
(d)
at 10am
that is when the curve indicates the begin of a change in the distance to home.
(e)
7.5 miles.
this is the point marked by a star on the graph.
down on the time scale this point shows 11:45am, and on the left side in the distance scale it shows 7.5 miles (the middle between 5 and 10 miles).
so, at that time she was still 7.5 miles away from home.
(f)
she traveled 40 miles to her grandmother (the left part of the curve from 0 distance until it turns flat), and then 40 miles back home (the right part of the curve from 40 distance all the way down to 0).
so, in total she traveled
40 + 40 = 80 miles
Jill always buys the same kind of shampoo in an 11.5-ounce bottle. She is at the store buying more and sees that the bottle is now bigger and has 20% more for the same price. How many ounces of shampoo are in the new bottle.
Answers
Step-by-step explanation:
100% = 11.5
20% more means 120%
120% = 100%×1.2 = 11.5×1.2 = 13.8 ounces
4
Elijah is given a birthday cake. He is rather selfish and does not share this cake with anyone
else. On the first day he eats 2/5 of the cake and on the second day he eats 3/7 of the cake. What
fraction of the cake is now left?
Answers
Answer:
6/35
Step-by-step explanation:
so he ate 2/5 first day, and the 3/7 the other day, so we need to add the 3/7 to 2/5.
they had to have the same number as their denominator.
so we gonna multiply (5) (3) and (5) (7) and also (7) (2) and (7) (5)
then we have 14/35 and 15/35 so we can add them together to find out 29/35
then we minus it from 35/35 to find out how much is left
35/35 - 29/35 is 6/35 , which is our answer
each child has 9 crayons.if there are 38 children ,how many crayons are there in total?
Answers
Answer:
342
Step-by-step explanation:
9x38=342, so the answer is 342 crayons
Answer:
342 crayons
Step-by-step explanation:
Each child has 9 crayons. This means each one of the children has 9 crayons for himself or herself. So if there are 38 children,it means each one of the 38 children has 9 crayons.
The total number of crayons is therefore gotten by multiplyiong the number of crayons of each child(9) by the total number of children(38).
∴38×9=342.
A dairy farmer plans to enclose a rectangular pasture (of length x and width y) adjacent to a river to provide enough grass for the herd, the farmer has 240m of fencing material. No fencing is required along the river. What should be the dimensions of the pasture that will provide the maximum area of pasture?
explain with steps. Tnx
Answers
Answer:
Step-by-step explanation:
The amount of fencing provided is 240 meters, and it only needs to cover 3 sides, as one side is the river and does not need to be fenced. 240/3 is 80, which is the length and width of the pasture. 80 is the length and width because squares have a larger area than rectangles if the perimeter is the same.
In conclusion, the pasture is a square with side length of 80. The dimensions of the pasture are 80x80
Hope this helped :)
i need help with this hard question
Answers
Answer:
Bottom left = 8
Top right = 15
Middle right = 25
Step-by-step explanation:
Total = 40
3 + 5 = 8
40 / 8 = 5
1 part = 5
5 x 3 = 15
5² = 25
A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. A rectangle is shown. The length of the top and bottom sides is 23 meters. The length of the left and right sides is 15 meters. A vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. Lines are drawn from the bottom left point to the top of the vertical line and from the bottom right point to the top of the vertical line. What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines? 21. 2 m 27. 5 m 32. 5 m 38. 2 m.
Answers
Approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
A 15-meter by 23-meter garden is divided into two sections. In this rectangle,
Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. The length of the top and bottom sides is 23 meters. The length of the left and right sides is 15 meters.Here, a vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. The length of the left side of the square will be 15 long. Thus, the lenght of its diagonal is,
[tex]d_1=15\sqrt{2}\\d_1=21.213\rm\; m[/tex]
The length of the sidewalk in smaller rectangle in the right side of figure is,
[tex]d_2=\sqrt{15^2+8^2}\\d_2=17\rm\; m[/tex]
Sum of the lengths of the two sidewalks using the pythagoras theorem is,
[tex]S=21.2+17\\S=38.2\rm\;m[/tex]
Thus, approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.
Learn more about the Pythagoras theorem here;
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Answer:
D 38.2
Step-by-step explanation:
E2020
¿Cuáles son los términos algebraicos que representan a una función cuadrática incompleta
con solamente término cuadrático?
Answers
Una ecuación cuadratica que solo tiene el termino cuadratico se escribe como:
y = a*x^2
¿Como escribir esta ecuación cuadratica?
La ecuación cuadratica general se escribe como:
y = a*x^2 + b*x + c
Donde el termino cuadratico es el primero, el segundo es el lineal y el tercero es el constante.
Entonces, si queremos una ecuación cuadratica que solo tenga el termino cuadratico, la ecuación sera:
y = a*x^2
Sí quieres aprender más sobre cuadraticas, puedes leer:
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Which inequality can be used to find how many $1.25 snack packs can be purchased for $10.00?
Answers
Answer:
1.25s [tex]\leq[/tex] 10.00
Step-by-step explanation:
Let's snack = s
Note:
[tex]\leq[/tex] ⇒ Less than or equal to
[tex]\geq[/tex] ⇒ Greater than or equal to
< ⇒ Less than
> ⇒ Greater than
Since we are trying to find how many $1.25 snack packs can be purchased for $10.00.. Thus, that less than or equal to $10.00 which also means we use [tex]\leq[/tex].
Thus the equation is 1.25s [tex]\leq[/tex] 10.00
`lenvy`
Answer:
8 snacks can be purchased
Step-by-step explanation:
10.00/1.25=8
Bob’s rectangular TV is 40 inches wide and 30 inches high. What is the length of the diagonal of Bob’s TV?
a.35 in.
b.45 in.
c.50 in.
d.70 in.
Answers
The length of the diagonal of Bob’s TV will be 50 in.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
Bob’s rectangular TV is 40 inches wide and 30 inches high.
Now,
Since, TV is in rectangular shape.
Hence, It satisfy the Pythagoras theorem.
Let the length of the diagonal of Bob’s TV = x
So, We can formulate;
⇒ x² = 40² + 30²
⇒ x² = 1600 + 900
⇒ x² = 2,500
⇒ x = √ 2,500
⇒ x = 50 in
Thus, The length of the diagonal of Bob’s TV = 50 in.
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Alex wonders if the same proportion of people are left-handed in the United States and Canada. He wants to
obtain a random sample of people from each country to test if there is a significant difference between the
proportion of left-handed people in each country.
Which of the following is an appropriate set of hypotheses for Alex's significance test?
Answers
Answer:
Pu.s - pc = 0
Pu.s -pc ≠ 0
(Answer D)
Step-by-step explanation:
Kahn
The appropriate set of hypotheses for Alex's significance test is option D.
What is Hypothesis Testing?Hypothesis testing is the testing of the relationship between two variables for something we needed to test.
There is null hypothesis and alternate hypothesis.
Null hypothesis, H₀ is the statement we need to test.
Alternate hypothesis, H₁, is true if null hypothesis is false.
Here, given that,
Alex wonders if the same proportion of people are left-handed in the United States and Canada.
He wants to obtain a random sample of people from each country to test if there is a significant difference between the proportion of left-handed people in each country.
H₀ : there is no significant difference
H₁ : there is a significant difference
So the correct option is,
H₀ : p(U.S) - p(C) = 0
H₁ : p(U.S) - p(C) ≠ 0
Hence the correct option is D.
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Swimming Pool On a certain hot summer's day, 163 people used
the public swimming pool. The daily prices are $1.25 for children
and $2.00 for adults. The receipts for admission totaled $257.00.
How many children and how many adults swam at the public pool
that day?
There were
children at the public pool.
Answers
I need help with the working
Answers
Answer:
288 cm^3.
Step-by-step explanation:
The volume of each small square = 2*2*2 = 8 cm^3
Each rectangular length of end 2*2 is made up of 12/2 = 6 squares.
There are 6 of these rectangular lengths.
So the volume = 6 * 6 * 8 cm^3
288 cm^3.
find cube root of 45324
Answers
the answer is
35.6540944227
Write the log equation as an exponential equation. You do not need to solve for x.
In (3x + 2) = 3x
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[tex]\ln(3x+2) = 3x\\\\\implies \log_e (3x+2) = 3x\\\\\implies e^{3x} = 3x+2[/tex]
-5x - 2y = 12 and 3x +2y = 8 using elimination as an ordered pair
Answers
Answer:
(-10, 19)
Step-by-step explanation:
Hey there!
In order to find the value of x and y, you need to make a system of equations
Now the question says to use elimination
The elimination method is when you make two values the same and then eliminate them with the proper sign: addition, subtraction, etc.
In this case, the step of making equal values is already done for us since there is 2y in both equations
[tex]-5x-2y=12\\3x+2y=8\\\\-2x=20\\x=-10\\[/tex]
What was done was called elimination
I added both equations together and when you add -2y and 2y, they eliminate each other
Now when you simplify the system, you get that x is equal to -10
Now we can substitute this value into the first or second equation
I am going to do the first equation
[tex]-5(-10)-2y=12\\50-2y=12\\-2y=-38\\y=19[/tex]
So after substituting the x value in the equation, we got the y value
Which is 19
So the solution to this system of equations is:
(-10, 19)
Find the solution of the system of equations.
-
5x – 4y = -9
10x– 7y = -22
Answers
Answer:
x = -5
y = -4
Step-by-step explanation:
5x - 4y = -9
10x - 8y = -18
10x - 7y = -22
-y = 4
y = -4
Substitue y into any equation
5x - (-16) = -9
5x = -25
x = -5
bellamy is building a gate to put on a fence. the gates measurements are 7 feet by 7 feet a diagonal wooden brace is going to be attached to keep the gate rigid what is the length of wood bellany needs to cut for the brace leave your answer in simplified radical form
Answers
The length of the diagonal is the hypotenuse of the fence
The length of the wood is [tex]7\sqrt{ 2[/tex] yards
How to determine the length of the wood?The dimensions of the fence are:
7 ft by 7 ft
The length (L) of the diagonal is calculated using:
[tex]L = \sqrt{a^2 + b^2[/tex]
This gives
[tex]L = \sqrt{7^2 + 7^2[/tex]
Express as products
[tex]L = \sqrt{7^2 * 2[/tex]
Express as radical
[tex]L = 7\sqrt{ 2[/tex]
Hence, the length of the wood is [tex]7\sqrt{ 2[/tex] yards
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Is -2 a whole number or irrational number?
Answers
Answer:
It is neither.
Step-by-step explanation:
A whole number is all numbers is 0, 1, 2, 3, 4.... you get it
An irrational number is a number that cannot be written as a fraction and -2 can be written as -2/1
The exponential function f(x) has a positive coefficient, a base of 0.6, and a horizontal asymptote at y = 3. If g(x) = 2(x - 3), which statement is true? A. The function f(x) represents exponential growth, and the function g(x) represents exponential decay. B. The function f(x) represents exponential decay, and the function g(x) represents exponential growth. C. The functions f(x) and g(x) both represent exponential growth. D. The functions f(x) and g(x) both represent exponential decay.
Answers
Answer:i don’t know the answer the answer but it’s f
Step-by-step explanation:
does anyone know the answer to this question?
Answers
Answer:
c = 2.5 , d = - 3
Step-by-step explanation:
f(x) = cx + d
f(4) = 7 ( substitute x = 4 into the equation and equate to 7 )
f(10) = 22 ( substitute x = 10 into the equation and equate to 22 )
4c + d = 7 → (1)
10c + d = 22 → (2)
subtract (1) from (2) term by term to eliminate d
(10c - 4c) + (d - d) = 22 - 7 , that is
6c = 15 ( divide both sides by 6 )
c = 2.5
substitute c = 2.5 into (1) and solve for d
4(2.5) + d = 7
10 + d = 7 ( subtract 10 from both sides )
d = - 3
Answer:
c = 2.5
d = - 3
Step-by-step explanation:
f(x) = cx + d
f(4) = 7
f(10) = 22
4c + d = 7
10c + d = 22
(10c - 4c) + (d - d) = 22 - 7
6c = 15
--- ----
6 6
c = 2.5
4(2.5) + d = 7
10 + d = 7
-10 -10
d = - 3
A rectangular yard measures 12 feet by 10 feet. Find the cost of installing a fence around the yard if the fence costs
$3.10 per foot
Answers
Answer:
$372
Step-by-step explanation:
12 × 10 = 120
1 foot = $3.10
120 feet = ?
120 feet × $3.10
= $372
$372÷ 1 foot = $372
Solve and check 5x-12=3x+24 (I’m so lost)
Answers
In this equation x=18
Work Shown:
5x-12=3x+24
Add 12 to both sides
5x-12+12=3x+24+12
Simplify
5x=3x+36
Subtract 3x from both sides
5x-3x=3x+36-3x
Simplify
2x=36
Divide both sides by two
2x/2 = 36/2
Simplify
x=18
Answer:
x=18
Step-by-step explanation:
1. Add 12 to both sides
5x-12 +12 = 3x+24 +12
2. Simplify
5x=3x+36
3. Subtract -3x from both sides
5x-3x=3x+36-3x
4. Simplify
2x=36
5. Divide both sides by same factor (2)
2x/2=36/2
6. Simplify
ANSWER: x=18
Ella’s test grades in her history class are 89, 94, 82, 84, and 98. What score must Ella make on her next test to have a mean test score of 90?
Answers
Answer:
the answer is 93
Step-by-step explanation:
mean of x,y,z
x+y+z
3 terms
(x+y+z)/3=mean
so
represent next test score as x
89+94+82+84+98+x
count how many terms ther are (6 terms)
mean is 90
(89+94+82+84+98+x)/6=90
add the like terms
(447+x)/6=90
multiply both sides by 6 to clear fraction
447+x=540
subtract 447 from both sides
x=93
How do you find the area of a triangle when given only the lengths of three sides?
Answers
Answer:
Use Heron's formula; see below.
Step-by-step explanation:
Use Heron's formula.
Let the sides of the triangle have lengths a, b, and c.
[tex] s = \dfrac{a + b + c}{2} [/tex]
[tex] area = \sqrt{s(s - a)(s - b)(s - c)} [/tex]
Example:
A triangle has side lengths 3, 4, and 5 units.
Find the area of the triangle.
[tex] s = \dfrac{a + b + c}{2} [/tex]
[tex] s = \dfrac{3 + 4 + 5}{2} [/tex]
[tex] s = 6 [/tex]
[tex] area = \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex] area = \sqrt{6(6 - 3)(6 - 4)(6 - 5)} [/tex]
[tex] area = \sqrt{6(3)(2)(1)} [/tex]
[tex] area = \sqrt{36} [/tex]
[tex] area = 6 [/tex]
573,297.88 rounded to the nearest 10
Answers
Answer:
573,300.00 to the nearest 10
Step-by-step explanation:
Kim says that 1/4 x 12 is the same as dividing 12 by 4 do you agree with Kim? explain your answer.
Answers
Answer:
yes i do
Step-by-step explanation:
1/4 x 12= 3
12 divided by 4 = 3
Find the area of the regular polygon. Give the answer to the nearest tenth.
Square with a radius of 13 m.
Answers
Answer:
338 m^2
Hope this helps!
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