Answer:
vertex = (- 3, - 1 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = - [tex]\frac{1}{2}[/tex] (x + 3)² - 1 ← is in vertex form
with vertex = (- 3, - 1 )
Solve for x and show all of your steps.
3x - 20 - 4x = 4x - (3x - 2)
Answer:
Step-by-step explanation:
3x -20 -4x =4x -(3x -2)
3x - 20 -4x = 4x -3x+2
-x-20 =x +2
-20-2=x +x
-22=2x
x= -22/2
x=-11
A rectangular lot is 50 meters wide and 90 meters long. Give the length and the width of another rectangular lot that has the same perimeter but a larger area.
Answer:
Length = 80 metres and Width = 60 metres.
Step-by-step explanation:
Given
Length = 90m
Width = 50m
Required
Dimension of another rectangle with the same perimeter but larger area;
Perimeter of a rectangle is calculated as thus;
[tex]Perimeter = 2(Length + Width)[/tex]
Substitute: Length = 90m and Width = 50m
[tex]Perimeter = 2(90m+ 50m)[/tex]
[tex]Perimeter = 2(140m)[/tex]
[tex]Perimeter = 280m[/tex]
Area of a rectangle is calculated as thus;
[tex]Area = Length * Width[/tex]
Substitute: Length = 90m and Width = 50m
[tex]Area = 90m * 50m[/tex]
[tex]Area = 4500m^2[/tex]
So, the implication of this question is to get a rectangle whose perimeter is 280m and area is greater that 4500m²
Using trial by error method;
Assume length of a rectangle is 80m;
This means the width must be 60m
Calculating the perimeter
[tex]Perimeter = 2(80m+ 60m)[/tex]
[tex]Perimeter = 2(140m)[/tex]
[tex]Perimeter = 280m[/tex]
Calculating the area
[tex]Area = 80m * 60m[/tex]
[tex]Area = 4800m^2[/tex]
Since, the area of this rectangle is greater than the area of the previous rectangle. we can adopt this dimension.
Length = 80 metres and Width = 60 metres.
Note: There are other dimensions that have higher area and exact perimeter as the given rectangle in the question;
A six-foot-tall basketball player shoots a ball towards the basket and misses. The height in feet of the ball up off the floor of the court as it travels through the air can be modeled by the function: [tex]h(x)=-16x^2+48x+6[/tex] where x is the number of seconds the ball is in the air after the shot is taken. When does the ball reach its maximum height? What is the maximum height of the ball? How much time will pass in seconds from the start of the shot to the ball hitting the floor? Answer all three questions to receive full credit.
Answer:
i) The maximum height of the ball 'x' = 1.5 seconds
ii) The maximum height = 42
Step-by-step explanation:
Step(i):-
Given h(x) = - 16 x² + 48 x +6 ...(i)
Differentiating equation (i) with respective to 'x'
[tex]h ^{l} (x) = - 16 (2 x) +48 (1)[/tex] ...(ii)
Equating Zero
- 3 2 x + 4 8 = 0
- 32 x = - 48
x = 1.5
step(ii):-
The maximum height of the ball 'x' = 1.5
Again Differentiating equation (ii) with respective to 'x'
[tex]h ^{ll} (x) = - 16 (2 x) < 0[/tex]
The maximum height 'x' = 1.5
h(x) = - 16 x² + 48 x +6
h(1.5) = - 16 (1.5)² +4 8 (1.5) +6
= 42
The maximum height at x = 1.5 is = 42
Final answer:-
i) The maximum height of the ball 'x' = 1.5 seconds
ii) The maximum height = 42
The accompanying stem-and-leaf plot represents Kiko's test scores this year. What is the median score for this set of data?
Answer: 80
Write down all the values and cross out until you get to the middle, since there are 2 values, find the mean, which would be 80
Please answerrrrrrr !!!! please
Who much time would it take for a train accelerating at 21.5 m/s2 to go from
13.2 m/s to 38.9 m/s?
Answer:
Step-by-step explanation:
v=u+at
38.9=13.2+21.5 t
21.5 t=38.9-13.2
21.5 t=25.7
t=25.7/21.5≈1.195 s
Answer:
To find the time taken, we use the equation:
v
=Then to find the time taken, we use the equation:
v = u + at
where:
v is the final velocity of the train
u is the initial velocity of the train
a is the train's acceleration
t is the time taken
So, we get:
t = (v-u)/a
t = (38.9 - 13.2)/21.5
t = 25.7/21.5
t = 1.19 seconds
When the two crews start working together, what part of all
the garbage bins will the first garbage truck empty?
The crew of a garbage truck takes 5 hours to empty all the
bins in one neighborhood on pickup day. The city assigned
a second garbage truck to this neighborhood. During their
training, it took the crew from the second truck 8 hours to
empty all the bins.
0.6
0.5
0.7
Time
(hours)
t
Part of Bins
Emptied
Rate
(part/hour)
1
5
0.4
First Truck
500
(9
1
t
Second
Truck
1
8
8
This question is not properly written
Complete Question
When the two crews start working together, what part of all
the garbage bins will the first garbage truck empty?
The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins.
Options
• 0.6
• 0.5
• 0.7
Answer:
0.6
Step-by-step explanation:
Let us say that the total hours worked by both trucks = t hours
Number of hours worked by first truck = 5 hours
Number of hours worked by second truck = 8 hours
Let 1 = total number of bins.
For the 1st truck the rate at which work was carried out is
(1 ) ÷ (5 ) = 1/5
For the 1st truck the rate at which work was carried out is
( 1 ) ÷ (8 ) = 1/8
Then,
(1/5 + 1/8) × t =1
(1/5 + 1/8) × t= 1
(13/40)t = 1
t = 1÷ 13/40
t = 1× 40/13
t = 40/13 hours.
Hence, the total hours worked by both trucks = 40/13 hours
the part of all
the garbage bins that the first garbage truck will empty is calculated as:
1/5 × 40/13 hr
1/5 × 40/13
= 0.6153846154
Approximately = 0.6
Therefore, when the two crews start working together, the part of all
the garbage bins that the first garbage truck will empty is 0.6 of the total work done.
Answer:
A) 0.6
Step-by-step explanation:
What are the coordinates of the vertex of the graph of the absolute value function h(x) = 3|x + 5| + 2? A) (5,-2) B) (-5,2) C) (5,2) D) (2,-5)
Answer:
B) Vertex = (-5, 2)
Step-by-step explanation:
Vertex can be defined as defined as the point where two lines meet and form a particular angle with each other. It can also be described as the point where a line changes its direction
We can find vertex by two methods:
1) GRAPHWe can see in the graph attached below that the line changes its direction at point (-5, 2). So the vertex is (-5,2)
2) FORMULAGeneral form of equation of mod function is given by
y = a |x - h| + k
where Vertex = (h, k)
The given equation is
h(x) = 3 |x + 5| + 2
h(x) = 3 |x - (-5)| + 2
where h = -5 and k = 2
So the vertex is:
Vertex = (-5, 2)
Answer:
(–5, 2)
Step-by-step explanation:
Object------------- Diameter (cm) ----- Circumference (cm)
Coin --------------------------- 3 ------------------------- 10
Flying disc -------------------23--------------------------- 28
Jar lid---------------------------- 8------------------------------25
Flower pot -----------------------15------------------------------47
Owen measured the diameter and circumference of four circles. Which one of his measurements is the least accurate?
Coin
Flying disc
Jar lid
Flower pot
Answer: Flying disc
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula for each object:
Circumference(C) = π x diameter
CoinDiameter = 3
Circumference (measured) = 10
C (calculated) = π x d = π x 3 = 9.42
10≅9.42
Flying discDiameter =23
Circumference (measured) = 28
C (calculated) = π x d = π x 23 = 72.25
72.25 ≠ 28
Not accurate
Jar lidDiameter =8
Circumference (measured) =25
C (calculated) = π x d = π x 8= 25.13
25 ≠ 25.13
Flower potDiameter =15
Circumference (measured)=47
C (calculated) = π x d = π x 15 = 47.12
47 ≠47.12
Feel free to ask for more if needed or if you did not understand something.
Answer:
Jar lid
Step-by-step explanation:
If you look up the diameter and circumference of the jar lid, it would give you an answer and if you compare it the answers are diffrent. So what you wan to put is: "I know that the Jar lid is wrong because For a jar lid, the diameter is 8, but for the circumference its is 2.5, and on the chart the dimeter is 8 BUT the circumference is 2.5" Hope this help. :)
Can someone please help me on these two questions?
Answer:
Arc = angle/360° x 2πr
13) = 72/360 x 2π x 25
= 1/5 x 2π x 25 = 10π
14) 270/360 x 2π x 2
= 3/4 x 4π = 3π
The surface area of a cube is 24 square inches.
What is the side length of the cube?
Answer:
2 inches
Step-by-step explanation:
A cube has 6 faces. Therefore, each face is 4 square inches. (24/6) The side length of the square (face of the cube) is the square root of the area. The square root of 4 is 2. There is your answer :)
Picture attachment below
Answer:
1/3
Step-by-step explanation:
the total outcomes is 3*4 = 12
the probability to get two digit numbers 14 or less is :
11 12 13 14
4/12 = 1/3
Mya says when 10 is added to a number, the hundreds digit stays the same. Is Mya's statement always true?
Answer:
no
Step-by-step explanation:
When you add 1 90+10 it equals 2 00. The hundreds digit, underlined, changed.
Answer:
the answer is no
Step-by-step explanation:
500+100=600
For f(x)= 4x+1 and g(x) = x^2 -5, find (f g)(x).
O A. 4x2 -19
O B. 4x3 + x2 - 4x -6
O C. 4x3 + x2 - 20x-5
O D. 4x3 + x2 - 5x -5
Answer:
The answer is option c.
4x³ + x² - 20x - 5
Answer:
C
Step-by-step explanation:
Please help this is about be getting a 4/4 in my math class now I have 3/4 I want to get 4/4 please help...
Answer:
Step-by-step explanation:
what is the answer for n ?
Answer:
18
Step-by-step explanation:
The formula for interior angles in a ngon is
(n-2)*180
2880/180=16
n-2=16
n=18
if you need to exercise 4 hours per week, how many minutes do you need to exercise each day to achieve this goal?
Answer:
A approximation of 34 minutes and 30 seconds each day .
Step-by-step explanation:
First you would need to convert 4 hours to minutes , so 1 hour equals 60 minutes - 60 min = 1 hour, 60 min times 4 = 240 minutes in total. There are 7 days in total of the week, 240 minutes - 7 days of the week : 240 divided by 7 , equals a approaximation of 34 minutes and 30 seconds each day.
You are a male who has a high school diploma. You plan to attend collage and earn a bachelors degree. When you graduate from college you get a job paying $40,780/yr. how much less areyou earning per year than median?
Answer: I think it’s 20,390
Step-by-step explanation:
Answer: 11,272
Step-by-step explanation: there are 52 weeks in a year multiply that by median wage, which is 1001. Then minus 40,780.
the pair of figures is similar. find x. round to the nearest tenth if necessary.
A: 34cm
B: 29.6cm
C: 9.8cm
D: 21.9cm
Answer:
B
Step-by-step explanation:
graph {x | x > 4} {x | x < -2} on a number line
Answer:
Step-by-step explanation:
well,
you mark an arrow to the left side of # line with open circle on -2
then,
you mark an arrow to the right side of # line with open circle on 4
Which expression represents the polynomial −2x3−4x2+2x4+3x+4 rewritten in standard form?
Answer:
10 x^4 - 8x^5
Explanation:
To write a polynomial in standard form, simplify and then arrange the terms in descending order. Ex. ax^2+ax+c
Then you would simplify
−2 x−5(x^2x^2)−2x4(x^2x^3)
Simplify each term
= 10 x^4 - 8x^5
what does DE equal to ?
Please help with my math
Answer: 9x-20
Step-by-step explanation:
The function is [tex]f(x)=3x-5[/tex], in order to obtain f(f(x)) you have to replace x in the function by the function itself:
[tex]f(f(x))=3(3x-5)-5=9x-15-5=9x-20[/tex]
This is for adding and subtracting polynomials, word problems. I have real difficulty with word problems in math, so please help me!
please see the attached picture for full solution
Hope it helps..
Write this polynomial in descending order: –4x5 + 4x3 + x7 – 10 + 2x4
I need some help for some questions.. (:
Answer: :
x7 –4x5 + 2x4+ 4x3 + x7 – 10
How many ways can the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members?
a.
Permutation; Subscript 28 Baseline P Subscript 4 Baseline = 491,400
b.
Permutation; Subscript 24 Baseline P Subscript 4 Baseline = 255,024
c.
Combination; Subscript 28 Baseline C Subscript 4 Baseline = 20475
d.
Combination; Subscript 24 Baseline C Subscript 4 Baseline = 10626
Answer:
A)[tex]^{28}P_4}=491400[/tex]
Step-by-step explanation:
Total number of members = 28
We are supposed to find the no. of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members
When 1 member is selected for Chairman position
So, 27 members will be left for the selection for the position of Vice chairman
When 1 member out of 27 is selected for Vice chairman position
So,26 members will be left for the selection for the position of secretary
When 1 member out of 26 is selected for secretary position
So,25 members will be left for the selection for the position of treasurer
Permutation relates to the act of arranging all the members of a set into some sequence or order,
The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter.
So, we will use permutation over here
Formula [tex]^nP_r=\frac{n}{(n-r)!}[/tex]
Substitute n = 28 and r = 4
So,[tex]^{28}P_4=\frac{28!}{(28-4)!}=491400[/tex]
So, Option A is true
A)[tex]^{28}P_4}=491400[/tex]
Hence There are 491400 ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members.
The number of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members is 491,400.
The given parameters
Number of members = 28 Number of positions = 4Total arrangement of the different positions available[tex]nP_r =\frac{n!}{(n- r)!}[/tex]
[tex]28 P4 = \frac{28!}{(28-4)!} = \frac{28!}{24!} = 491,400[/tex]
Thus, the number of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members is 491,400.
Learn more about permutation here: https://brainly.com/question/3086912
Which of the following points lies on the line y=x?
(-4,4)
(2,-2)
(-4,-4)
(-2,2)
Answer: -4, -4
Step-by-step explanation:
y=x means x and y are the same number in the coordinate, no matter if it’s positive or negative.
Use the drop-down menus to complete each statement to describe the relationship
between the number of inches and the number of centimeters.
Answer:
Step-by-step explanation:
2.54 centimeters = 1 inch
15.24 centimeters = 6 inches
I don't know what other relationships they want :)
PLEASE ANSWER ASAP 10 points WILL MARK THE BRAINIEST!
Mr. Smith paid $36.36 for a carpet. This amount includes a tax of 10%. What was the cost of the carpet before tax?
Answer:
32.72
Step-by-step explanation:
36.36/100
0.3636
0.3636 times 90 (I use 90 because 100-10=90) 10% tax, so 90% original cost.
32.72