We can see (either graphically or algebraically) that the lowest point, or minimum, occurs when x = 3 and y = −4. That is the location of the vertex.
The coordinate of the vertex is (3 , −4)
given equation
y = [tex]x^{2}[/tex] - 6x + 5
= [tex](x - 3)^{2}[/tex] - 4
We can see (either graphically or algebraically) that the lowest point, or minimum, occurs when x = 3 and y = −4. That is the location of the vertex.
The coordinate of the vertex is (3 , −4)
quadratic function :
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape. The picture below shows three graphs, and they are all parabolas.
All parabolas are symmetric with respect to a line called the axis of symmetry. A parabola intersects its axis of symmetry at a point called the vertex of the parabola.
You know that two points determine a line. This means that if you are given any two points in the plane, then there is one and only one line that contains both points. A similar statement can be made about points and quadratic functions.
To learn more about quadratic function:
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solve for x . Leave your answer in the simplest form
Hello!
Here we are given a composite shape, meaning that we can divide this shape up into ways that we are given formulas to solve for legs and such.
I can see here that this can be divided into a triangle and a rectangle using a horizontal line.
The leg lengths of this triangle would be 9, because it is congruent to the bottom side of the rectangle, and 7, because it is the left side minus the right side.
This would also make a right triangle, meaning we could solve for the hypotenuse utilizing the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
[tex]6^2+7^2=c^2[/tex]
[tex]36+49=c^2[/tex]
[tex]c^2=85[/tex]
[tex]c=\sqrt{85}[/tex]
Which is in simplest radical form.
Hope this helps!
HELP PLEASE Quadratic Equations Math Nation
Answer:
its 5/6
Step-by-step explanation:
we just group things around and we have this
36 m^2 - 60 m = -25
Alternate forms:
12 m (3 m - 5) = -25
36 m^2 - 60 m + 25 = 0
Solution:
m = 5/6
explain how you can tell whether a group of ratios represents a proportional relationship. PLEASE HELP
The diagram shows a right-angled triangle.
All the measurements are in centimetres.
The area of the triangle is 18cm^2
Work out the length of the shortest side of the triangle.You must show all your working
Answer:
short side = 4
Step-by-step explanation:
area = 1/2BH
18 = 1/2(x - 1)(x + 4)
18 = 1/2(x² + 4x - x - 4)
multiply both sides of the equation by 2:
36 = x² + 3x - 4
x² + 3x - 40 = 0
(x + 8)(x - 5) = 0
x = 5
short side = 5 - 1 = 4
The shortest length of the right angled triangle is 4 cm.
Area of a triangle:area = 1 / 2 bhwhere
b = base
h = height
Therefore,
area = 18 cm²
18 = [tex]\frac{1}{2}[/tex] × (x - 1)(x + 4)
36 = (x - 1)(x + 4)
x² + 4x - x - 4 = 36
x² + 3x - 4 = 36
x² + 3x - 4 - 36 = 0
x² + 3x - 40 = 0
x² - 5x + 8x - 40 = 0
x(x - 5) + 8(x - 5) = 0
(x + 8)(x - 5) = 0
x = -8 or 5
we can only use positive numbers.
Therefore,
x = 5
The shortest sides is definitely one of the 2 legs . The hypotenuse of a triangle is the longest side.
Therefore,
h = x - 1 = 5 - 1 = 4 cm
b = x + 4 = 5 + 4 = 9 cm
learn more on right angled triangle here: https://brainly.com/question/2292567?referrer=searchResults
please help me and no links this is due in 10 mins ill give you the crown
Answer:
angle Q is 68°
angle R is 112°
8) The total weight of 15 boxes is 45 pounds. How much would 40 boxes weigh?
Answer:
120 pounds I think
Step-by-step explanation:
Answer:
120 pounds
Step-by-step explanation:
[tex]\frac{15}{45}[/tex] = [tex]\frac{40}{x}[/tex] so then you would cross multiply : 15x=40 times 45
and then solve: 15x= 1800
x= 120
The volume, V, of any cube with side length, s, can be determined using the formula V = s3 . What is the volume, in cubic centimeters, of a cube with a side length of 0.2 centimeters?
A
3.2
B
0.6
C
0.006
D
0.008
PLSSSS DO NOT GIVE ME FILES
Read the sentences.
Some people train by climbing and swimming. Others train with running, biking, and weightlifting.
Select the sentence that correctly combines these sentences using semicolons.
Some people train by climbing and swimming, others train with running; biking; and weightlifting.
Some people; train by climbing and swimming, others train with running, biking, and weightlifting.
Some people train by climbing and swimming; others train with running; biking; and weightlifting.
Some people train by climbing and swimming; others train with running, biking, and weightlifting.
Please help me thank you!
The function ƒ(x) = 2x − 2 indicates:
a shift to the right of 1 unit.
a shift to the left of 2 units.
a shift to the right of 2 units.
None of these choices are correct.
Answer:
None of the choices are correct
Step-by-step explanation:
This is because it should be going down if it was subtracting but no answer says that so
Can someone please help me with this and if able to explain how I work it out please
Answer:
4 = [tex]\sqrt{15[/tex]
Step-by-step explanation:
help!! tell whether the triangle is a right triangle- i don’t need an explanation thank you!!
Answer:
1.) Right triangle
2.) Not right triangle
3.) Not right triangle
4.) Not right triangle
5.) Right triangle
6.) Right triangle
Step-by-step explanation:
The ones that are a right triangle have at least one angle that has an L shape
16. The boys' soccer to a bouchoccer ball conoccer balls for $391. If the team bought a total of 17
soccer balls, how much did each soccer ball cost?
A. $21
B. $23
C. $374
D. $408
Answer:
The answer is B $23.
Step-by-step explanation:
You take 391 and divide it by 17
391/17=23
Hope this helps!
The function f(x) = 6x + 8 is transformed to function g through a horizontal stretch by a factor of 5. What is the equation of function g? Replace the values of a and k in the function equation
Answer:
[tex]g(x) = \frac{6}{5}x + 8[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 6x + 8[/tex]
[tex]k = 5[/tex] --- horizontal stretch factor
Required
Find g(x)
When a function is stretched horizontally by k, the resulting function will be:
Rule: [tex]g(x) = f(\frac{1}{k}x)[/tex]
So, we have:
[tex]g(x) = f(\frac{1}{5}x)[/tex]
Solve for: [tex]f(\frac{1}{5}x)[/tex]
[tex]f(\frac{1}{5}x) = 6 * \frac{1}{5}x + 8[/tex]
[tex]f(\frac{1}{5}x) = \frac{6}{5}x + 8[/tex]
Recall that:
[tex]g(x) = f(\frac{1}{5}x)[/tex]
[tex]g(x) = \frac{6}{5}x + 8[/tex]
Answer:
f(1/5x) = 6 ^1/5x +8
Step-by-step explanation:
A horizontal stretch by a factor of 5 means that the input, or x, is multiplied by : 1/5
please help me, I lost my answer
Can someone please help me with math.
Answer:
the answer to the questions are c,b,a
Janet and Artie want to play tug-of-war.
Artie pulls with 200 pounds of force while
Janet pulls with 60 pounds of force. In
order to make this a fair contest, Janet
enlists the help of her friends Trudi, Sherri,
andyBridget who pull with 20, 25, and 55
pounds respectively. Write an inequality
describing the minimum amount Janet's
fourth friend, Tommy, must pull to beat
Artie.
Answer:
Tommy would have to pull at least 40.0000000..... something to beat Artie but the closest whole number is 41 becouse it has to be over 200
Step-by-step explanation:
200 /= 60 + 20 +25 + 55 + x
200/= 160 + x - 160 both sides
40 = x
A cylindrical container has a radius of 7 feet and a height of 2 feet. What is the volume of the container to the NEAREST WHOLE FOOT?
Answer:
308 feet ^3
Step-by-step explanation:
Volume of a cylinder: V=πr^2h
Substituting radius = 7 and height = 2:
V = π (7)^2 (2) = 307.88 ~= 308 feet ^3
I will give you BRAINLIEST for the correct answer
Answer:
48 in³
Step-by-step explanation:
volume=length*breadth*height
=12*2*2
Susan deposits $100 into a savings account that earns simple interest at a rate of 5%. If she makes no withdrawals, how much total interest has Susan's savings account earned after 5 years?
Answer:
Interest is $25
Step-by-step explanation:
Formula to find interest:
I = Prt
Given:
P = 100
r = 5% or 0.05
t = 5
Work:
I = Prt
I = 100(0.05)(5)
I = 5(5)
I = 25
Solve.
Pls need help
Answer: try C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
It's c because you multiply 3 1/8 by 3 and 3 1/4 by 4 and 3 1/2 by 1.
Mrs. Kirsch went shopping at a department store. The store is having a sale, discounting all items by 30% off the marked price. She decides to buy an item originally marked $85.95. She also had to pay 6% sales tax. What is the sales tax on the item? What is the final cost (sale price plus tax) of her purchase?
Answer:
63.76
Step-by-step explanation:
85.95-30% 60.16
60.16+6% 63.76
BRAINLIEST-
Find the volume of the figure
Answer:
4080cm²
Step-by-step explanation:
Find the x and y intercept of y=0.5x^2-3x.
Step-by-step explanation:
i don't have a step by step explanation so here you go the answer
Write a true equation based on this diagram
What is the slope of the line through ( 10, 1) and (0,4)?
khan Academy
Answer:
-1/2
Step-by-step explanation:
[tex]y^{2} = -4 \\y^{1} =-1\\x^{2} = 0\\x^{1} = -10[/tex]
Using the formula [tex]\frac{y^{2}-y^{1} }{x^{2}-x^{1} }[/tex]
[tex]\frac{-4-1}{0-(-10)}[/tex]
Simplifly
[tex]\frac{-5}{10} = \frac{-1}{2}[/tex]
Help! The picture is with it to see the question
Answer:
8
Step-by-step explanation:
sqrt8*sqrt8 = sqrt8^2 = 8
ill give brainiest - please help ASAP with WORK FOR IT please and thank you!! :)
3 pages, with work pleasee
Answer:
isosceles trapezoidtrapezoidrhombussquarerectangleparllelogramquadrilateral10x+18+62=180 co interior angle10x=180-80
x=100/10=10
:.x=10
9.
8x+2=7x+14 corresponding angle of parallelogram are equal
8x-7x=14-2
x=12
10.
4x+4=5x+1 corresponding sides of parallelogram are equal
4-1=5x-4x
x=3
11.
4+3x=19corresponding sides of parallelogram are equal
3x=19-4
x=15/3
x=5
28.4 grams = ? ounces
If a triangle with the angles of 72 degrees, 62 degrees, and 46 degrees and one of the side lengths is 40, what would the length of the other two side be?
Answer:
The length of the other two sides are: 43.09 and 32.60
Step-by-step explanation:
Let the given side of the triangle be b(= 40), and the angles be;
A = [tex]72^{o}[/tex], B = [tex]62^{o}[/tex]and C = [tex]46^{o}[/tex].
Applying the Sine rule,
[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]
So that,
[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex]
[tex]\frac{a}{Sin 72}[/tex] = [tex]\frac{40}{Sin62}[/tex]
a = [tex]\frac{0.9511*40}{0.8829}[/tex]
= 43.0898
a = 43.09
Also,
[tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{40}{Sin62}[/tex] = [tex]\frac{c}{Sin46}[/tex]
c = [tex]\frac{0.7193*40}{0.8829}[/tex]
= 32.5881
c = 32.60
The length of the other two sides are: 43.09 and 32.60
HELP ME PLEASEEEEEEE I WILL GIVE BRAINLIEST PLZ HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answer:
pretty simple, you should get 1824
Step-by-step explanation:
first find area of square, you should get 1536 in^2. Then triangle, the formula is base times height divided by 2. lmk if you need more help