Considering the vertex of the quadratic function, it is found that:
A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the function is given by:
y = 0.75x² - 13.5x + 57.75.
Which means that the coefficients are a = 0.75 > 0, b = -13.5, c = 57.75.
Thus, the minimum value is given by:
[tex]y_v = -\frac{(-13.5)^2 - 4(0.5)(57.75)}{4(0.75)} = -22.25[/tex]
Thus:
A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.
More can be learned about the vertex of a quadratic function at https://brainly.com/question/24737967
Manuel starts with $30. He earns $8.00 per hour plus an additional
bonus of $12 each day. He spends $8.00 for lunch. If he has $94 at
the end of the day, how many hours did he work?
Answer:
He worked about 5.5 hours
Step-by-step explanation:
Im pretty sure
Answer:
7.5 hours
Step-by-step explanation:
h=hours
30+8h +12-8 =94
8h+34=94
8h =60
h= 7.5
what is 2 multiplied 34 times plus 72 divided 3
Answer:
92
Step-by-step explanation:
2 × 34 + 72 ÷ 3
(2 × 34) + (72 ÷ 3)
68 + 24 = 92
I hope this helps!
You can calculate the width of the lake using a surveying technique, as shown in the diagram. Find the width of the lake.
Step-by-step explanation:
Angles XVW and XYZ are congruent, and so are angles VWX and XZY by the alternate interior angles theorem.
This means that triangle VWX is similar to triangle YZX.
So, since corresponding sides of similar triangles are proportional, VW/XY = WX / XZ.
120/8 = 15 = WX / 6.
So the width is 90 m.
If the number of bacteria in a colony doubles every 336 hours and there is currently a
population of 9,000 bacteria, what will the population be 672 hours from now?
bacteria
The population of bacteria after 672 hours is 36000.
What is unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
According to the given question we have
The number of bacteria double is 336 hours.
And, the current population of bacteria is 9,000.
Therefore,
The population of bacteria after 336 hours = 9,000×2 = 18,000
⇒ the population of bacteria after 672 hours = 18000 × 2 = 36000
Hence, the population of bacteria after 672 hours is 36000.
Learn more about Unitary method here:
https://brainly.com/question/22056199
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Match each word to its definition.
Answer:
1. biased sample: sample not representative of the entire population
2.convenience sample: sample where representatives are easily accessible
3.unbiased sample: sample where every member of the population has an equal chance
4. self-selected sample: sample where members volunteer to take part
5. stratified sample: members are selected from the different subgroups within a population
6. systematic sample: sample members are selected through the use of a rule.
Hope this helps!!
1. biased sample: sample not representative of the entire population
2.convenience sample: sample where representatives are easily accessible
3.unbiased sample: sample where every member of the population has an equal chance
4. self-selected sample: sample where members volunteer to take part
5. stratified sample: members are selected from the different subgroups within a population
6. systematic sample: sample members are selected through the use of a rule.
Hope this helps!!
Plss help will give Brainliest!!!!
Answer:
1/6
Step-by-step explanation:
if the mean of 4 6 9 11 10 and k is 8 what is its median
HELPPPP 80 POINTS
Solve the right triangle.
Round your answers to the nearest tenth
answer:
A=46°
a=17.983 (tenths- 18, hundredths- 17.98)
b=17.366 (tenths- 17.4, hundredths- 17.37)
explanation:
1. find angle A
it shows that the angle corresponding with the side length of 25 is a right angle, meaning it's 90°. using that information and the angle given to us (44°), we're able to find the missing angle. since all the angles in a triangle always add up to 180°, we can add the two angles together and then subtract that from 180° to find the missing angle.
90°+44°=134°
180°-134°=46°
A=46°
2. find side a
using the law of cosines, we're able to find the length of side a. cosine of an angle equals [tex]\frac{adjacent}{hypotenuse}[/tex]. we'll be using angle B (44°) for our angle. after we plug in the values, we can just solve the equation to find side a.
cosine44°=[tex]\frac{a}{25}[/tex]
(multiply both sides by 25)
25cosine44°=a
a=17.983
3. find side b
finding the length of side b is very similar to how you found side a. you can use the law of cosines again (make sure you use the right side lengths and angles!), but i used the law of sines. the sine of an angle equals [tex]\frac{opposite}{hypotenuse}[/tex]. we're going to be using the same angle for this.
sine44°=[tex]\frac{b}{25}[/tex]
(multiply both sides by 25)
25sine44°=b
b=17.366
--
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A teacher bought 12 sheets of stickers to use on the homework of her students. Each sheet had 48 stickers. At the end of the year, the teacher had 123 stickers remaining.
Estimate how many stickers the teacher used.
Answer:
453
Step-by-step explanation:
12×48=576 (number of stickers she has)
576-123=453 (number of stickers she had-number of stickers she had left)
find the area of the circle.
diameter=8 inches
Answer:
Area = 32 π in^2
Step-by-step explanation:
Area of the Circle : Area = 2 *π * r^2
diameter = 2 *radius
8 inches = 2 * radius
radius = 8 in/2 = 4 in
radius = 4 in
Area = 2 *π * r^2
Area = 2 *π * (4 in)^2
Area = 2 *π * 16 in^2
Area = 32 π in^2
Answer:
If you're using the exact number for pie then the answer is approximately 50.27. If you're using 3.14 for pie then the answer is 50.24.
m/5 = 25
That is my question
Step-by-step explanation:
m / 5 = 25
m = 25 × 5
m = 125
.............
Answer:
125
Step-by-step explanation:
m/5 = 25
m = 25 x 5
m = 125
express the following rational algebraic expression to its simple form.show your solution
4. ײ - 1 / ײ - 2×+1
Answer:
[tex]\dfrac{x+1}{x-1}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{x^2-1}{x^2-2x+1}[/tex]
Factor the numerator and denominator
[tex]\implies \dfrac{(x+1)(x-1)}{(x-1)(x-1)}[/tex]
Factor out the common term [tex](x-1)[/tex]:
[tex]\implies \dfrac{x+1}{x-1}[/tex]
[tex]\rm{blue{ANSWERANSWERANSWERANSWERANSWERANSWERANSWERANSWER:}}[/tex]
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\rm The\ answer\ is \rightarrow \red{\dfrac{x + 1}{x - 1}}[/tex][tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]blue{\boxed{ \red{\rm {CarryOnLearning!}}}}[/tex]
Which equation is the correct translation of the following statement?
Four less than a number is nine.
O 9 - X= 4
O9-4 = x
O x-4 = 9
O4 - X= 9
Let the number be x.
subtract 4:-
x-4 (4 less)
this expression equals 9:-
x-4=9 (Option C)
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.
Answer:
The Last option
Step-by-step explanation:
We see this figure has eight faces, so we already know the answer choice is D, because answer choice D is the only option with 8 faces.
Now let's prove this using Euler's Formula
F = Faces
V = Vertices
E = Edges
We see 12 vertices, 8 faces, and 18 edges. Now plug in the formula.
F + V = E + 2
8 + 12 = 18 + 2
20 = 20
Find the greatest number of children to whom 260 pens and 364 chocolates can be divided equally.
answer:
52
explanation:
52 is the highest shared factor of the two numbers.
52*5=260
52*7=364
--
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Colin predicted whether he got answers right or wrong in his 50 question exam.
He identified the 18 questions he thought he got wrong.
It turns out that Colin got 3 questions right that he thought he got wrong.
Colin also got a total score of 27 out of 50 in the test.
What is the percentage accuracy he had with predicting his scores?
Answer:
65.2%
Step-by-step explanation:
Explanation is in photo.~Hope this helps~
can someone help me with these three questions pls
Answer:
Step-by-step explanation:
#1. right 5 units
#2. down 2 units
#3. The translation rule is (5, -2)
The swiss mathematician leonhard euler and the french mathematician rene descartes both discovered a pattern in the numbers of edges, vertices, and faces of polyhedrons. solve problems 810.
Answer:
I am stuck on this two
Step-by-step explanation:
rectangle, 6 8 14 12
Round to the nearest tenth: 3.732
A. 3.7
B. 3.74
C. 3.73
D. 3.8
Pleasee i need these answers fast!!
Answer:
Rounded to the tenth: 3.7
Hope this helped!
Answer:
the answer is a
Step-by-step explanation:
3.7
Philippe went to the farmer's market and spent $2.35 on apples, $1.85 on bananas, and $3.10 on blueberries. How much did Phillipe spend in total? (3 points) a $7.30 b $7.55 c $8.30 d $8.55
Answer:
a. $7.30
Step-by-step explanation:
2.35 + 1.85 + 3.10 = 7.30
What is the volume of this cone?
Use ≈ 3.14 and round your answer to the nearest hundredth
Answer:
100 cubic centimetres
Step-by-step explanation:
Volume of Cone = 1/3 pie r^2 h
= 1/3 × 3.14 × 4 × 4 × 7
= 117.226
= 100 cubic centimetres ( nearest hundredth)
In a bag there are 2 red marbles, 3 white marbles and 5 blue marbles. Once a marble is selected, it is NOT replaced. Find the P(Blue then Red). Write your answer as a percent rounded to the nearest whole number.
Answer:
For each draw, it is the number of that color, divided by the total number of marbles. For more than one draw, just multiply the fractions.Take a look at what I did. It should become clear.
Step-by-step explanation:
What is the greatest common denominator of 24 and 25
Answer:
1
Step-by-step explanation:
The only number 24 and 25 can both have is 1
What is the area of the unshaded part of the rectangle to the right?
A. 19,000 ft²
B. 45,000 ft²
C. 28,000 ft²
D. 26,000 ft²
Answer:
D 26000
Step-by-step explanation:
100 x 100 = 10000
120 x 150 = 18000/2 = 9000
150 x 300 = 45000
10000 + 9000 = 19000
45000 - 19000 = 26000
Bonjour je ne comprend pas cette exercice; si quelqu'un peut m'aider je suis preneuse.
Merci d'avance
Answer:
0,24 m
Step-by-step explanation:
La table est un rectanble donc l'angle en haut à droite est de 90°.
Tu connais donc un angle et le côté opposé à l'angle et tu cherche le côté adjacent.
On sait que tan(â) = [tex]\frac{Cote oppose}{Cote adjacent}[/tex] donc :
tan(40)= [tex]\frac{1,27}{x}[/tex]
[tex]\frac{1,27}{tan(40)} = x[/tex]
donc x ≈ 1,51 m
Le trou du mileu est à [tex]\frac{2,54}{2}[/tex] soit 1,27m du bord.
Donc elle doit taper à 1,51 - 1,27 = 0,24m du trou du milieu.
j'espère avoir été clair.
HELP ME PLEASE!!
Solve the simultaneous equations.
x + 2y = 13
x + 5y = 28
x =
y=
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-Here, We have given two equations that is ,[tex]\sf{ x + 2y = 13\:\: and\:\: x + 5y = 28}[/tex]To Find :-We have to find the value of x and y.Concept used :-Linear equations are those equations which having highest power of degree as 1 .Linear equations can be solved by subsitute method, elimination method and cross multiplication method. Here, I have used substitution method to make calculation easier. In subsitute method, you have to subsitute the value of one variable of eq(1) in eq(2) .Let's Begin :-Here,
We have two equations, let consider these two equations as eq(1) and eq(2) that is,[tex]\sf{ x + 2y = 13 ...eq(1)}[/tex]
[tex]\sf{ x + 5y = 28 ...eq(2)}[/tex]
By solving eq(1) :-
[tex]\sf{ x + 2y = 13 }[/tex]
[tex]\sf{ x = 13 - 2y ...eq(3)}[/tex]
Subsitute eq(3) in eq(2) :-
[tex]\sf{ (13 - 2y) + 5y = 28 }[/tex]
[tex]\sf{ 13 - 2y + 5y = 28 }[/tex]
[tex]\sf{ 13 + 3y = 28 }[/tex]
[tex]\sf{ 3y = 28 - 13 }[/tex]
[tex]\sf{ 3y = 28 - 13 }[/tex]
[tex]\sf{ 3y = 15 }[/tex]
[tex]\sf{ y = }{\sf{\dfrac{ 15}{3}}}[/tex]
[tex]\sf{ y = }{\sf{\cancel{\dfrac{ 15}{3}}}}[/tex]
[tex]\bold{ y = 5 }[/tex]
Thus, The value of y is 5
Now,Subsitute the value of y in eq(1) :-
[tex]\sf{ x + 2(5) = 13 }[/tex]
[tex]\sf{ x + 10 = 13 }[/tex]
[tex]\sf{ x = 13 - 10 }[/tex]
[tex]\bold{ x = 3 }[/tex]
Hence, The value of x and y are 5 and 3 .
[tex]\bold{\huge{\underline{ Let's \: Verify }}}[/tex]
Equation 1 :-[tex]\sf{ x + 2y = 13 }[/tex]
[tex]\sf{ 3 + 2(5) = 13 }[/tex]
[tex]\sf{ 3 + 10 = 13 }[/tex]
[tex]\sf{ 13 = 13 }[/tex]
[tex]\bold{ LHS = RHS }[/tex]
Equation 2 :-[tex]\sf{ x + 5y = 28 }[/tex]
[tex]\sf{ 3 + 5(5) = 28 }[/tex]
[tex]\sf{ 3 + 25 = 28 }[/tex]
[tex]\sf{ 28 = 28 }[/tex]
[tex]\bold{ LHS = RHS }[/tex]
Let's use elimination method
Subtract eq(2) from eq(1)We get
[tex]\\ \rm\Rrightarrow 2y-5y=13-28[/tex]
[tex]\\ \rm\Rrightarrow -3y=-15[/tex]
[tex]\\ \rm\Rrightarrow y=\dfrac{-15}{-3}[/tex]
[tex]\\ \rm\Rrightarrow y=5[/tex]
Putting on eq(1)
[tex]\\ \rm\Rrightarrow x+2y=13[/tex]
[tex]\\ \rm\Rrightarrow x+2(5)=13[/tex]
[tex]\\ \rm\Rrightarrow x+10=13[/tex]
[tex]\\ \rm\Rrightarrow x=13-10[/tex]
[tex]\\ \rm\Rrightarrow x=3[/tex]
(x,y)=(3,5)[tex]\LARGE{\underbrace{\underline{\rm{Verification:-}}}}[/tex]
[tex]\\ \rm\Rrightarrow x+2y=13[/tex]
[tex]\\ \rm\Rrightarrow 3+2(5)=13[/tex]
[tex]\\ \rm\Rrightarrow 3+10=13[/tex]
[tex]\\ \rm\Rrightarrow 13=13[/tex]
And
[tex]\\ \rm\Rrightarrow x+5y=28[/tex]
[tex]\\ \rm\Rrightarrow 3+5(5)=28[/tex]
[tex]\\ \rm\Rrightarrow 3+25=28[/tex]
[tex]\\ \rm\Rrightarrow 28=28[/tex]
Hence verified!
HELPPPP WHATS THE AREA
Answer:
the answer is 42
Step-by-step explanation:
you multiply the sides to get the area
100 points HELP (EASY)
Answer:
6 inches
Step-by-step explanation: I did the test
Answer
HEY :) do you want hep with all f them or just some of the awnsers
Step-by-step explanation:
Question five What is the perimeter? Use 3.14 for pi. Please Show Work! I Will Mark As Brainlest!!
Answer:
73.81
Step-by-step explanation:
You know that the formula for circumeference is 2(pi)r.
2x3.14x11=69.08;
However, a part of the circle is cut off, leaving 3/4 of it.
3/4x69.08=51.81.
However, you add the 11+11 to it because of the slice.
22+51.81=73.81
Question
Find the circumference of the circle. Round your answer to the nearest hundredth.
The circumference is about
inches.
Answer:
Circumference of a cicle in terms of radius:
Circumference = 2·π·r = 2·3.14·3 = 18.85(*)
In terms of diameter:
Circumference = π·d = 3.14·6 = 18.84(*)
In terms of area:
Circumference C = √4·π·A = √4·π·28.27 =18.85
Step-by-step explanation:
radius= 3in.
to find:the circumference of the circle.
solution:formula C=2πr
=2·π·3
≈18.84956in
nearest hundredth= 18.85in
