The vertex form which is equivalent to the provided quadratic function of variable x is (x-1)²+3.
What is the vertex form of parabola?Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point.
The function given in the problem is,
[tex]f(x) = 4+x^2 - 2x\\f(x) = x^2 - 2x+4[/tex]
Add and subtract (-1)² in the above function,
[tex]f(x) = x^2 - 2x+4+(-1)^2-(-1)^2\\f(x) = x^2 - 2x+(-1)^2+4-1[/tex]
Use the formula of whole square,
[tex]f(x)=(x-1)^2+3[/tex]
This is the required vertex form.
Hence, the vertex form which is equivalent to the provided quadratic function is (x-1)²+3.
Learn more about the vertex form of the parabola here;
https://brainly.com/question/17987697
can anyone help me with this.
Links, and files will be deleted.
Answer:
32
Step-by-step explanation:
Triangle angle = 180
First we add!
58 + 90 + c = 180
148 + c = 180
Now we subtract!
180 - 148 = c
32 = c
Have an amazing day!!
Please rate and mark brainliest!
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS THANKS PLS ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS THANKS PLS ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS THANKS PLS ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS
Answer:
I think it would be 1/8 but that is a strong maybe
A group of climbers begin climbing at an elevation of 6500 feet and ascend at a steady rate of 600 vertical feet per hour. what is their elevation after 3.5 hours?
Two numbers whose sum is 29 and their difference is 15
Answer:
22 and 7
Step-by-step explanation:
Let x and y be the two numbers we are looking for:
The statement “their sum is 29” means x + y = 29
The statement “their difference is 15” means x - y = 15
we get this system:
x + y = 29 (1)
x - y = 15 (2)
Let’s solve it :
(1) + (2) ⇒ x + y + x - y = 29 + 15 ⇒ 2x = 44 ⇒ x = 44/2 = 22
Now we replace x by 22 in equation (1) :
22 + y = 29 ⇒ y = 29 - 22 = 7
David draws one card from a deck of cards. What is the probability that he selects a 7?
4/52 = 1/13
hope it helps...!!!
EASY POINTS!!
Question 4 of 10
True or false? The graph represents a function
A. True
B. False
SUBMIT
ps: This is a quadratic function of equation
[tex]f(x) = - x {}^{2} + 4[/tex]
Find the volume of the cone, round your answer to the nearest tenth
Answer:
V ≈ 78.54
Step-by-step explanation:
A meat-seller sells x kg of ducks at $8.50 per kg and (2x + 5 ) kg of chicken at $3.60 per kg. If he collects a total of $206.40, find the value of x.
Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
1) Set up an equation that involves all of the values; the price and kg of each duck and chicken equating to 206.40.
[tex]8.50(x) + 3.60(2x + 5) = 206.40[/tex]
[tex]8.50x + 7.2x + 18 = 206.40[/tex]
2) Solve it.
[tex]15.7x + 18 = 206.40[/tex]
[tex]15.7x = 206.40 - 18[/tex]
[tex]15.7x = 188.4[/tex]
[tex]x = \frac{188.4}{15.7}[/tex]
[tex]x = 12[/tex]
There are 3 children of a lady. In how many ways is it possible to dress them for a party if the first child likes 3 dresses, second likes 4 and the third likes 5 but the third child has out grown one of them? Each child has a different set of clothes.
A. 11
B. 10
C. 60
D. 48
E. 15
ty!
If all of their dresses are fit for the kids, the possible way to dress them is 3*4*5=60
But one dress is out grown for the third child. Hence, the combination that are not possible.
3*4*1=12
So total number of possible ways are :
3*4*5 - 3*4*1=48
Hence the answer is option D.
I need the answer please!
Answer:
5 units
Step-by-step explanation:
Let's assume point (5,1) to be C
according to the picture we know AC= 3 and BC=4
Applying pythagorean theorem: a^2+b^2=c^2
(AC)^2+(BC)^2=(AB)^2
3^2+4^2=(AB)^2
9+16= (AB)^2
AB^2=25
AB=5
which is an equation of the axis of symmetry of the graph of the equation y= x^2-6x+2?
1) x=-3
2) y=-3
3) x=3
4) y=3
Answer:
x=3
Step-by-step explanation:
The equation is written in the form ax2+bx+c. As you can see, a=1, b=-6 and c=2. The axis of symmetry is worked out by x=−b2a.
−(−6)2(1) = 62=3
Substituted this value of x back into the equation to find the y coordinate.
y=(3)2−6(3)+2
y=9−18+2
y=−7q
So the vertex of the line is at (3,-7)
PLSSS HELP IF YOU TURLY KNOW THISS
Write both fractions in terms of a common denominator. In this case, it's the least common multiple of 6 and 12, which is 12 = 2•6. So multiply the first fraction by 2/2, then simplify:
[tex]\dfrac46 - \dfrac3{12} = \left(\dfrac22\times\dfrac46\right) - \dfrac3{12} = \dfrac{2\times4}{2\times6}-\dfrac3{12} = \dfrac8{12}-\dfrac3{12} = \dfrac{8-3}{12} = \boxed{\dfrac5{12}}[/tex]
What is the factored form of x^3-1? A. (x^3-1) (x^2 + x + 1) B. (x - 1) (x^2 - x + 1) C. (x - 1) (x^2 + x +1 ) D. (x^3 - 1) (x^2 + 2x + 1)
Answer:
C. (x - 1) (x^2 + x +1 )
Step-by-step explanation:
x^2 +x +1
x x^3 x^2 x
-1 -x^2 -x -1
If you multiply it out it equals the answer
PLEASE HELP!!
For systems of inequalities, graph each system on a coordinate plane to show the solution region. Next, use the graph to answer the question. Be sure to define your variables and show all of your work.
Q.1. The potter at a pottery store makes two sizes of vases. The larger size takes six hours to make, and the smaller size takes 1.5 hours to make. The potter works 30 hours a week. She needs to make at least six total vases a week, including at least two of each size. Give one example of how many of each type of vase the potter can make.
Answer:
Step-by-step explanation:
Let x and y be the large (x) and small (y) vases the potter makes in one week.
We are told that the large and small vases require 6 hours for each large(x) and 1.5 hours for each small (y) vase. The combination of large and small vases made in one week thus requires a total time of:
6x + 1.5y = total hours/week
We are told that the potter works 30 hours per week, so:
6x + 1.5y = 30 hours
We also learn that she needs to make at least 6 vases in a week, so:
x + y => 6
Plot the two equations:
6x + 1.5y = 30, and
x + y => 6
This will produce the attached grap, Vases1. The inequality appears as the shaded area in the upper area. Any point in the shaded area satisfies the inequality of x + y => 6. The x and y intercepts are at (0,6) and (6,0), representing either all large (x) or small vases (y).
The lines intersect at (4.67,1.33). This represents a fictional combination of 4.67 large and 1.33 small vases. This results in 6 vases (4.67 + 1.33) that require a total of 30 hours to make (6*4.67 + 1.5*1.33) = 30 hours. If you want to select whole number answers, they appear at (0,6), (2,4), (4,2), and (6,0). (x,y or large,small). All combinations result in 6 vases, but eould require less than the 30 hours of time available. Any whole number combination in the area below the line 6x + 1.5y = 30, but above the line x+y =>6 are valid, such as (4,4). This area is shown in Vases2. The valid area for making choices has the darkest shade, where the two inequalities are both satisfied.
help please will mark brainly when can
let a,b,c, and d be integers select yes or no to indicate whether each number is a possible product for a/b • c/d
8.96 [ yes ] [ no ]
[tex]5 \sqrt{6} [/tex]
[ yes ] [ no ]
15 [ yes ] [ no ]
[tex] \binom{\pi}{4} [/tex]
[ yes ] [ no ]
The expression a/b * c/d is an illustration of number types
The truth value of 8.96 is yesThe truth value of 5√6 is noThe truth value of 15 is yesThe truth value of π/4 is yesHow to determine the true values of the numbers?The expression is given as:
a/b * c/d
Next, we test the given numbers
(a) 8.96
Express 8.96 as a fraction
8.96 = 896/100
Express the numerator and the denominator as products
8.96 = (224 * 4)/(50* 2)
Split the fraction
8.96 = 224/50 * 4/2
The above equation shows that 8.96 can be written in the form a/b * c/d.
Hence, the truth value of 8.96 is yes
(b) 5√6
Express 5√6 as a product expression
5√6 = 5 * √6
Evaluate the product
5√6 = 12.2474.....
The result of 5√6 is a non-terminating decimal
Hence, the truth value of 5√6 is no
(c) 15
Express 15 as a fraction
15 = 90/6
Express the numerator and the denominator as products
15 = (9 * 10)/(3 * 2)
Split the fraction
15 = 9/3 * 10/2
The above equation shows that 15 can be written in the form a/b * c/d.
Hence, the truth value of 15 is yes
(d) π/4
Express π as 22/7
π/4 = 22/7/4
Rewrite the expression as products
π/4 = 22/7 * 1/4
The above equation shows that π/4 can be written in the form a/b * c/d.
Hence, the truth value of π/4 is yes
Read more about numbers at:
https://brainly.com/question/24670740
What is the mode of the teachers' ages?
Answer:
55
Step-by-step explanation:
Use the key to find the ages:
24, 26, 28, 28
33, 36, 36
40, 40 , 47, 47, 48
52, 53, 55, 55, 55, 56, 57, 58
63, 64, 64
Find the greatest number of common ages: 55
Helpppppp i need a correct answer please make sure you are correct!! 50 points!
which angle has its terminal side on the positive y-axis?
2pi radians
pi radians
pi/2 radians
3 pi/2 radians
Answer:
[C] [tex]\frac{\pi }{2}\;radians[/tex]
Step-by-step explanation:
The ray in the terminal position, after the rotation is call the "terminal side of the angle."
Note that quadrant of the unit circle of any given angle the radians would be in:
Quad I → 0 < θ < pi/2
Quad II → pi/2 < θ < pi
Quad III → pi < θ < 3pi/2
Quad IV → 3pi/2 < θ < 2pi
Hence, Answer is [C] pi/2 radians
~lenvy~
please solve this paper
Answer:
1. the, from, although, won't he, ourselves
2. The father said to his son that he was happy with him. My laptop has been stolen by somebody. He wants to die in the village where he was born.
3. was, worked
Step-by-step explanation:
Hope this helps!
13. A triangle has angle measurements of
36°, 36° and 108°. Is the triangle acute, obtuse
or right? How do you know?
a , b , c , d ???????????????????
Answer:
First, add the two mixed numbers together.
[tex]1 + 2 = 3[/tex]
[tex]4/7 + 3/14 = 11/14[/tex]
Combine the equation and number.
[tex]3 + 11/14 = 3 \frac{11}{14}[/tex]
[tex]3\frac{11}{14} + 1/2 =[/tex] 4 2/7
Therefore, the answer is 1/2
I need help answering this question
Answer:
x -2 y + 2
Step-by-step explanation:
Latonya was just hired as an engineer for an electric company. she will make a salary of $50,000 a year. how much of latonya's salary will be taxed at the 10 percent rate? how much of latonya's salary will be taxed at the 28 percent rate?
The $5000 will be taxable amount at 10% of Latonya's salary, and $14000 will be taxable amount at 28% of Latonya's salary.
What is the income tax rate?It is defined as the tax rate applied on the solely earned money by a single entity.
Latonya salary per year = $50,000
If Latonya's salary will be taxed at the 10% rate, then she needs to pay tax:
[tex]= $50,000\times10\%[/tex]
[tex]=50000\times \frac{10}{100}[/tex]
[tex]= \$ 5000[/tex]
If Latonya's salary will be taxed at the 28% rate, then she needs to pay tax:
[tex]= \$50,000\times28\%[/tex]
[tex]=50000\times \frac{28}{100}[/tex]
[tex]= \$14000[/tex]
Thus, the $5000 will be taxable amount at 10% of Latonya's salary, and $14000 will be taxable amount at 28% of Latonya's salary.
Learn more about the income tax here:
brainly.com/question/17075354
15 POINTS: What is the slope of the line that passes through the points (a, b) and (c, b)?
Answer:
0
Step-by-step explanation:
[tex]slope \: of \: a \: line = \frac{y2 - y1}{x2 - x1} = \frac{b - b}{c - a} = \frac{0}{c - a} = 0[/tex]
what is the area of the triangle
Answer:
390
[tex]\frac{26x30}{2} =390[/tex]
Hope This Helps! :)
The time t required to empty a water tank varies inversely as the rate of pumping p. A pump can empty a water tank in 40 min at the rate of 120 gal/min. Write the equation of the inverse variation. How long it will take the pump to empty the water tank at the rate of 200 gal/min?
the question requires:
the time t required.
the equation of the inverse variation.
how do find t:
first we determine how much the tank holds by multiplying 120 by 40.
the tank holds 4800 gallons.
so now to find t we can use the formula v = d/t where d is the 4800 gallons.
so: t = d/v
t = 24 minutes
now for the equation of the inverse variation.
we can say that the equation is t = d/v since t and v are inversely proportional.
note that v and t stand for velocity and time respectively.
make sure to ask if you need any further guidance!!
Answer:
t = 24
Step-by-step explanation:
PLS HELP !!!! No links pls and Ty <3333
Answer:
45.2pi inches
Step-by-step explanation:
C=2×pi×r
since the answers already have pi we don't need to multiply it
C=2×22.6 = 45.2pi inches
Answer:
A. 22.6π
Step-by-step explanation:
Given:
22.6 inches across = diameter
What we need to find is how much ribbon do we need, so we use the formula:
C = 2πr
C = Circumference
r = radius = half diameter
Since we know the diameter, we do half of it to get the radius
22.6 ÷ 2 = 11.3
radius = 11
Now we substitute this into the formula:
C = 2πr
Substitute radius into formula
C = 2π(11.3)
Multiply 2 and 11.3
C = 22.6π
Find the product. 5(-3)=
Answer:
-15
Step-by-step explanation:
-15
Solution:A positive number times a negative number is a negative number.The product of 2 numbers means we multiply these numbers.Therefore, the product of 5 and -3 is-15Hope it helps.
Do comment if you have any query.
∆DEF≈~ STU. If TU-=8, SU = 10, and ST= 4, what is the length of -DE-?
a.10
b.8
c.4
d.cannot be determined
Answer:
if that statement is true, then DE=ST, and ST=4 so your answer should be DE=4
Explanation:
you can tell that they are even from looking at the first statement, it states DEF=STU, emphasizing on the DE=ST part, it gives your the answer right there because ST=4
Answer:
the answer is C.
Step-by-step explanation:
I know this because i am smart...
And katie is going to delete this so id.k why im even trying but #yolo
`
`
`
TOri
Trina is making quilts for sewing class. She will use 21 yards of yellow fabric, 10.1 yards of green fabric, and 24.8 yards of blue fabric. This amount makes 26 quilts. How many yards are used for each quilt?
Answer:
6.7 per unit
Step-by-step explanation:
A crate of apples that usually costs
$40 is on sale for 20% off. What is
the sale price for the crate of
apples?
Answer:
$32
Step-by-step explanation:
Step-by-step explanation:
We are trying to find $40 on sale for 20$ off.
40*20/100
40*0.2
You save=$8
40-8
Final Price=$32