The quadratic function given when converted to vertex form will be: [tex]f(x) = 2(x-11)^2 -57[/tex]
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.
For this case, the given quadratic function is:
[tex]f(x) =2x^2 -44x + 185\\[/tex]
Converting this to the vertex form, we get:
[tex]f(x) =2x^2 -44x + 185\\\\f(x) = 2(x^2 -22x) + 185\\f(x) = 2(x^2 -2 \times 11 \times x + 11^2 - 11^2) + 185\\f(x) = 2((x-11)^2 -121) + 185\\f(x) = 2(x-11)^2 -242 + 185\\f(x) = 2(x-11)^2 -57[/tex]
Thus, the quadratic function given when converted to vertex form will be: [tex]f(x) = 2(x-11)^2 -57[/tex]
Learn more about vertex form of a quadratic equation here:
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100 points. Please help. I'll give brainliest.
A: 95 people dislike both
B: 81
C: 21
Answer:
Thanks for the points!!
Step-by-step explanation: dawggggggg
SHOW WORK
To make purple paint, we need to maintain a 3:2 ratio of red paint to blue paint. Red paint costs $20 a gallon and blue paint costs $25 a gallon. A coupon gives a 10% discount on red paint and a 20% on blue paint. If you have $500 for paint, what is the maximum amount of red blue paint you can buy to make purple paint?
Answer:
red (w/discount) ... $18 per gallon
blue (w/discount) ... $20 per gallon
(3 n * 18) + (2 n * 20) ≤ 500
54 n + 40 n ≤ 500 ... 94 n ≤ 500 ... n ≤ 5 15/47
3 n = 15 gal red ... 2 n = 10 gal blue
Two species of birds are being compared. Species A can fly 18.9 miles in 42 minutes, while species B can fly 20.3 miles in 58 minutes. Which species is slower, and at what speed can it fly?
A Species A is slower, and it can fly 0.35 miles per minute.
B Species A is slower, and it can fly 0.45 miles per minute.
C Species B is slower, and it can fly 0.35 miles per minute.
D Species B is slower, and it can fly 0.45 miles per minute.
100 POINTS
Answer:
Option C .
Step-by-step explanation:
Here it is given that there are two species of birds which fly at different rates.
Species A can fly 18.9 miles in 42min .Species B can fly 20.3miles in 59min .We can use the formula here ,
[tex]\longrightarrow \red{ Speed =\dfrac{Distance} {Time} }[/tex]
For Species A :-
Substitute the respective values in stated formula ,
[tex]\longrightarrow v_A = \dfrac{18.9\ miles}{42min}\\[/tex]
Simplify ,
[tex]\longrightarrow v_A = 0.45\ miles / min [/tex]
For species B :-
Substitute the respective values in stated formula,
[tex]\longrightarrow v_B =\dfrac{20.3\ miles}{58min}\\ [/tex]
[tex]\longrightarrow v_B = 0.35\ miles / min [/tex]
Therefore from above calculations we can say that ,
[tex]\underline{\underline{ v_A > v_B }}[/tex]
Species B is slower and it can fly 0.35miles/minute .
Point \blue{A}Astart color #6495ed, A, end color #6495ed is at \blue{(-1, 8)}(−1,8)start color #6495ed, left parenthesis, minus, 1, comma, 8, right parenthesis, end color #6495ed and point \green{B}Bstart color #28ae7b, B, end color #28ae7b is at \green{(7, 3)}(7,3)start color #28ae7b, left parenthesis, 7, comma, 3, right parenthesis, end color #28ae7b. What is the midpoint of line segment \overline{AB} AB start overline, A, B, end overline?
Answer:
[tex]M = (3,5.5)[/tex]
Step-by-step explanation:
Given
[tex]A = (-1,8)[/tex]
[tex]B = (7,3)[/tex]
Required
Determine the midpoint
This is calculated as thus
[tex]M = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where:
[tex](x_1,y_1) = (-1,8)[/tex]
[tex](x_2,y_2) = (7,3)[/tex]
So, we have:
[tex]M = (\frac{-1+7}{2},\frac{8+3}{2})[/tex]
[tex]M = (\frac{6}{2},\frac{11}{2})[/tex]
[tex]M = (3,5.5)[/tex]
Hence;
The midpoint is (3,5.5)
Answer:
(0,0.5)
Step-by-step explanation:
Trust me I got it right on Khan
In Exercises 15-18, find the measure of the exterior
angle. (See Example 3.)
15.
75°
64°
2
Applying the exterior angles theorem, the measure of the exterior angle is: m∠2 = 139°.
What is the Exterior Angles Theorem?The exterior angles theorem states that the measure of the two remote angles in a triangle is equal to the measure of the exterior angle of a triangle.
Thus:
75° and 64° are remote interior angles.
Therefore:
m∠2 = 75° + 64°
m∠2 = 139°
Learn more about exterior angles theorem on:
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The scale of a map says that 8 cm represents 5 km. What distance on the map in centimeters representan 5 km
Answer:
8cm
Step-by-step explanation:
8cm = 5km
5km = 8cm
therefore 8cm represent 5km on the map
Find the value of x. Then classify the triangle by its angels
Answer:
x=134
Step-by-step explanation:
As angles in a triangle add up to 180 degrees
also angles on a straight line add up to 180
so 180-(64+70)=46
and 180-46=134
PLEASE GIVE BRAINLIEST AND THANKS
Which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Select three answers.
Answer:
y = 1/10x+60.
Step-by-step explanation:
Which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Select three answers. The correct answers are: The y-intercept of the function is $60. The function can be represented by the equation y = 1/10x+60.
Hope it helps!!!Brainliest pls!!!Thanks for the help <3
The full form of HA is Hypotenuse-angle and it states that if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
Answer ⤵️Hypotenuse of both triangles are equal.The acute angles formed on them are also equal since the sides are equal.Hence, Proved.
Answer:
HA
Step-by-step explanation:
Usually HA congruence is used in right angle triangles .as One common 90° right angle is present if Hypotenuse and adjacent angle remains similar the triangles are similar.
Please help!
A building is constructed on top of a cliff that is 300 meters high. A person standing on level ground below the cliff observes that the angle of elevation to the top of the building is 72° and the angle of elevation to the top of the cliff is 63°.
a. How far away is the person from the base of the cliff?
b. What is the building’s height?
The distance from the person to the base of the cliff is 269.78 meters.
The height of the building from the base of the cliff is 829.37 meters
The situation forms right angle triangle.
The building is constructed on top the cliff that is 300 meters high.
Right angle triangle:Right angle triangle has one of its sides as 90 degrees. Therefore, the sides can be found using trigonometric ratios.
The height of the building from the cliff is 300m. let's find the hypotenuse side of the angle of elevation formed to the cliff.
Using sin rule,
300 / sin (72 - 63) = y / sin (180 - 162)
300 / sin 9 = y / sin 18
300 sin 18 = y sin 9
y = 300 sin 18 / sin 9
y = 92.7050983125 / 0.156
y = 594.230769231
Therefore, how far the person to the base of the cliff can be calculated as follows;
cos 63 = adjacent / hypotenuse
cos 63 = x / 594.2307
x = 594.2307 cos 63
x = 269.775092454
x = 269.78 meters
Therefore, the distance from the person to the base of the cliff is 269.78 meters.
height of the cliff / 269.78 = tan 63
height of cliff = 269.78 tan 63
height of cliff = 529.37493165
height of cliff = 529.37
The height of the building = 300 + 529.37 = 829.37493165 = 829.37 meters
learn more on right triangle here: https://brainly.com/question/14806301
H 125°
D 180
3. A triangle has two sides that have lengths of
14 feet and 22 feet. Which of the following
lengths could not represent the length of the
third side?
A 8 ft
B 12 ft
c) 14 ft
(D) 20 ft
Step-by-step explanation:
14 ft hope this hellped ask again
A sheet of origami paper is in the shape of a square with a side length of 7 inches, as shown. What is the area of the sheet of origami paper? A square has side lengths of 7 inches. Use the formula for the area of a square, A = s squared, where A represents the area and s represents the side length. 14 Inches squared 28 Inches squared 49 Inches squared 98 Inches squared
Answer:
Its 49 inches.
Step-by-step explanation:
We know that a squares has 4 equal sides, therefor: all sides equal 7 inches.
To find the area, multiply 7x7- which is 49.
Formula: A=s squared -> 49=7 squared
Hope this helps, brainliest is always appreciated! :)
Have a great day! cx
~Mitsuna
James has 30 doughnuts. He eats 29. How many does he have left?
Answer:
1
Step-by-step explanation:
30
-29
-----
1
the answer is one
Answer:
the answer is 1
Step-by-step explanation:
39
-29
——
01
what's the answer?
3(9+6)+55
Answer:
=> 100
Step-by-step explanation:
=> 3(9+6)+55
=> 3(15)+55
=> 45 +55
=> 100
As a chef in a restaurant you have a recipe that uses 4 cups of flour to make 3 dozen cookies. You want to
make 12 dozen cookies, how many cups of flour do you
need?
Answer:
sorry its a little hard to answer your thing
Step-by-step explanation:
need ponits
13) through: (0, -1) and (-5,-1)
A) x + 3y = 3
B) x - 3y = 1
C) 5r - 3y = -3
D) y=-1
Answer:
y=-1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-(-1))/(-5-0)
m=(-1+1)/-5
m=0/-5
m=0
y-y1=m(x-x1)
y-(-1)=0(x-0)
y+1=0
y=0-1
y=-1
What is the complementary angles, one angle on is 2 degrees larger than the second angle?
Answer:
44 and 46
Step-by-step explanation:
A complementary angle is 90 degrees
90/2 = 45
If 45 + 45 = 90
44 + 2 = 46
44 + 46 = 90
:)
Combine these radicals.
Answer:
[tex]14\sqrt{5}[/tex]
Step-by-step explanation:
[tex]8\sqrt{5}+2\sqrt{45}[/tex]
[tex]=8\sqrt{5}+2\sqrt{9\cdot5}[/tex]
Use radical rule [tex]\sqrt{a \cdot b}=\sqrt{a}\sqrt{b}[/tex]
[tex]=8\sqrt{5}+2\sqrt{9}\sqrt{5}[/tex]
[tex]=8\sqrt{5}+2\cdot3\sqrt{5}[/tex]
[tex]=8\sqrt{5}+6\sqrt{5}[/tex]
[tex]=(8+6)\sqrt{5}[/tex]
[tex]=14\sqrt{5}[/tex]
Combine these radicals
8√5 + 2√45
O 4√5
O 10√5
O 14√5 ✓
8√5 + 2√45⇢2√5(4 + √9)⇢2√5(4+3)⇢2√5 x 7⇢14√5O 74√5
Which of the following can be used to show that these triangles are congruent?
Find the perimeter of the right triangle. If necessary, round to the nearest tenth.
a.25 mi
b. 60 mi
c. 150 mi
d. 300 mi
Please help me asappppp
Answer:
<5 ~= <1 - Corresponding Angles Theorem
<1 ~= <7 - Alternate Exterior Angles Theorem
<5 ~= <7 - Vertical Angles Theorem
line I || line m - Transitive Property
Is the relationship between the time spent swimming and the number of weeks proportional? Complete the statements
Answer:
lie on goes
Step-by-step explanation:
answer is Lie On For First And Goes For Second
What is the answer -10b-7=9?
i think it should be -1.6
if you add 7 to 9 it'll be 16.
if you divide -10 by 16 it'll give you -16/10.
simplify it and you should get -8/5 or -1.6.
Can someone help me please, thanks.
Answer: 2.19 pounds
Step-by-step explanation:
35 / 16 is 2.1875, if you round that you get 2.19
What is (f - g)(x)?
f(x) = -3x2
g(x) = -5x + 3
Write your answer as a polynomial or a rational function in simplest form.
Work Shown:
(f - g)(x) = ( f(x) ) - ( g(x) )
(f - g)(x) = ( -3x^2 ) - ( -5x+3 )
(f - g)(x) = ( -3x^2 ) - ( -5x) - ( 3 )
(f - g)(x) = -3x^2 + 5x - 3
What is the scale factor from Figure A to Figure B? PLEASE HELP
Answer:
Its 3 bro
Step-by-step explanation:
my guy A is just B scaled 3 times, every number on B times 3 equals their counterpart in A
PLLLLLLLLLLLLLLLLLLLLLLLZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answer:
Step-by-step explanation:
" ... at most 5 " ⇒ 5 is max value
[tex]\frac{x}{3}[/tex] ≤ 5
my question goes if your good at rounding what is 98.488578018 rounded
Answer:
Im not sure what you want it to be rounded but heres the answers:
Whole number: 98
Tenths: 98.5
Hundredths: 98.49
Thousandths: 98.489
Step-by-step explanation:
A human hair has an average diameter of about 0.000017 meter. Write this measurement in scientific notation.
Answer: 1.7 x 10-5
Step-by-step explanation:
Slove for x to the nearest tenth
Step-by-step explanation:
Let me start off by saying that 1 unit side is absolutely useless.
You can translate the 6 unit side downwards, so now we have a right isosceles triangle of 2 equal sides which are 6
The hypotenuse is given here by x.
Applying the Pythagorean theorem i can then say;
[tex]x {}^{2} = 6 {}^{2} + 6 {}^{2} [/tex]
[tex]x {}^{2} = 36 + 36[/tex]
[tex]x {}^{2} = 72[/tex]
[tex]x = \sqrt{72} = 6 \sqrt{2} = 8.485[/tex]
x=8.5
rounded to the nearest 10 :)