Answer:
2,1,4,3,6,5,8,7
Step-by-step explanation:
Given:
2,1,4,3,6,5,8,___
Pairing the sequence in twos
2,1
4,3
6,5
It can be seen that each pair of the sequence is arranged in descending order (from highest to lowest)
1, 2 is written as 2,1
3, 4 is written as 4,3
5, 6 is written as 6, 5
Then the next two numbers
7, 8 will be written as 8,7
2,1,4,3,6,5,8,7
Complete the square to write each equation in vertex form. Then, state whether the vertex is a minimum or a maximum and give its coordinates.
Answer:
a) y = (x + 1)^2 - 3
b) minimum
c) (-1, -3)
Step by step:
We start with the equation:
y = x^2 + 2*x - 2
First, we want to complete the square to write the equation in the vertex form.
y = (x - h)^2 + k
Such that the vertex is (h, k)
To complete the square, we can write this as:
y = x^2 + 2*1*x - 2
Now we can add and subtract 1
y = x^2 + 2*1*x + 1 - 1 - 2
y = (x^2 + 2*1*x + 1) - 3
The thing inside the parentheses can be written as:
x^2 + 2*1*x + 1 = (x + 1)^2
Then the quadratic equation will be written as:
y = (x + 1)^2 - 3
This is the vertex form.
b) Now we want to know if the vertex is a minimum or a maximum.
Remember that the leading coefficient tells use if the graph of the function opens up or down.
If the leading coefficient is positive, the graph opens up (then the vertex is a minimum)
If the leading coefficient is negative, the graph opens down (then the vertex is a maximum)
In this case, we can write:
y = 1*(x + 1)^2 - 3
The leading coefficient is 1, positive.
Then the vertex is a minimum.
c) The coordinates of the vertex are:
Remember that in the vertex form:
y = (x - h)^2 + k
the vertex is (h, k)
Then the vertex of our equation is:
(-1, - 3)
A bunch of ballons contains many different colors. red 17 purple 11 orange 3 green 1 yellow 2 What is the probability that a randomly selected balloon will be red? Write your answer as a fraction or whole number.
Answer: 1/2
Step-by-step explanation:
Number of red balloons = 17
Number of purple balloons = 11
Number of orange balloons = 3
Number of green balloons = 1
Number of yellow balloons = 2
Total number of balloons = 34
The probability that a randomly selected balloon will be red will be:
= Number of red balloons/Total number of balloons
= 17/34
= 1/2
Approximately how tall is the streetlight? Round your answer to the nearest tenth.
Note: your teacher may not want you to enter "feet" and instead may just want the number only.
===================================================
Work Shown:
tan(angle) = opposite/adjacent
tan(40) = h/20
20*tan(40) = h
h = 20*tan(40)
h = 16.7819926 which is approximate
h = 16.8
The streetlamp is approximately 16.8 ft tall.
When using your calculator, make sure it's in degree mode. One way to check is to compute something like tan(45) and you should get 1 as a result.
PLEASE HELP ASAP!! will mark!find the zeros of the function. no links
the answer is x=-1 or x= 5
Steve ran a 26-mile race at an average speed of 4 miles per hour. If Adam ran the same race at an average speed of 3 miles per hour, how many minutes longer did Adam take to complete the race than did Steve?
Answer:
Adam took 132 minutes longer than Steve.
Step-by-step explanation:
Let's find the time that takes Steve and Adam to complete the race. We will use the equation:
[tex] V = \frac{d}{t} [/tex]
Where:
d: is the distance = 26 miles
t: is the time =?
V: is the speed
For Steve we have the following time:
[tex] t_{s} = \frac{d}{V_{s}} = \frac{26 mi}{4 mi/h} = 6.5 h*\frac{60 min}{1 h} = 390 min [/tex]
And the time of Adam is:
[tex] t_{a} = \frac{d}{V_{a}} = \frac{26 mi}{3 mi/h} = 8.7 h*\frac{60 min}{1 h} = 522 min [/tex]
So, the difference between the time of Adam and Steve is:
[tex] \Delta t = t_{a} - t_{s} = 522 min - 390 min = 132 min [/tex]
Hence, Adam took 132 minutes longer than Steve.
I hope it helps you!
Look at pictures please
Answer:
5 x 3 x 2 = 30 feet
Step-by-step explanation:
Multiply all given lengths (has to be 3) in order to get the volume.
Find the volume of a given solid
object where the radius of base
is 7 cm and height is 12 cm.
Note: Consider the solid object is a cylinder because the radius of base and height of the solid is given.
Given:
Radius of base = 7 cm
Height = 12 cm
To find:
The volume of the given solid.
Solution:
The volume of a cylinder is:
[tex]V=\pi r^2h[/tex]
Where, r is the radius of the base and h is the height of the cylinder.
Putting [tex]r=7,h=12,\pi=\dfrac{22}{7}[/tex] in the above formula, we get
[tex]V=\dfrac{22}{7}\times(7)^2\times (12)[/tex]
[tex]V=22\times 7\times 12[/tex]
[tex]V=1848[/tex]
Therefore, the volume of the given solid is 1848 sq. cm.
A rectangular patio has a volume of 360 cubic feet. If the width is 8 feet and the length is 15 feet, what is the height of the patio stones?
Answer:
3 feet
Step-by-step explanation:
Volume of a rectangular object = length x width x height
360 = 8 x 15 x height
360 = 120 x height
height = 360 / 120
height = 3ft
Casey spends $29.00 on coffee each month. About how much dose Casey spend on coffee over 7 months ?
Answer:
203 dollars
Step-by-step explanation:
29 x 7
PLZZ HELPP RATIONALL OR NOTTTT
Answer:
1. [tex]\sqrt{7}[/tex]
2. The square root of an imperfect square
Step-by-step explanation:
A rational number is any number that can be written as a fraction (with the numerator and denominator being integers). All terminating and repeating decimals are rational.
The square root of an imperfect square is always irrational.
All the DJ’s that Marie interviewed for the party charged a flat fee for supplies and then charged per hour. One DJ was going to charge $200 for travel and music and then $10 per hour. The other DJ was going to charge $150 and then $15 per hour. How many hours would both DJ’s be the same price and what is that price?
the ball rolls downhill, its kinetic energy increases and its potential energy ________
Maximum
Minimum
.
The Ball Rolls Downhill, It's Kinetic Energy Increases And It's Potential Energy Maximum.
Hope Helps! :)
[tex] \: \: [/tex]
Adrian purchased a new car in 2007 for $27, 100. The value of the car has been
depreciating exponentially at a constant rate. If the value of the car was $12, 300 in
the year 2013, then what would be the predicted value of the car in the year 2023, to
the nearest dollar?
Answer:
2344 .
Step-by-step explanation:
n/a
If a car's gas tank has 15 gallons of gas in it, and the gauge says the tank is 75% full, then how many gallons can the entire tank hold?
12
20 gallons
24
11.25
Answer:
20 gallons
Step-by-step explanation:
set up proportion
15/x=75/100
cross multiply
75x=1500
x=20 gallons
1. An open box is to be made from a sheet of card 40cm by 30cm. A square of side x cm is to be
cut from each corner, as shown in the diagram, and then the sides will be folded up so that the
depth of the box will be x cm.
(a) Find in terms of x the length and width of the base of the box (ie AB and AD).
(b) The volume of the box is y. Write down an equation expressing y in terms of x.
Step-by-step explanation:
AB = DC = 40 - 2x
AD = BC = 30 - 2x
there is not more explanation possible, I think.
we cut off from each side 2 pieces of x cm. so, AB, DC, AD, BC are the the remaining lengths.
the volume of the box is ground area times height (x is the length of the remaining flaps after the cut, so, when folding up these flaps/sides, they will be x cm high).
Volume = y = AB×AD×x
=> y = (40-2x)×(30-2x)×x = (1200 - 60x - 80x + 4x²)×x =
= (1200 - 140x + 4x²)×x = 4x³ - 140x² + 1200x
1. A state is considering adding another character to their vehicle license plates in order to increase the number of license plates available. Currently, a license plate must have exactly six character spaces. Each character space may be filled with any capital letter other than I or O or any number between, and including, 0 to 9. Letters and numbers may repeat on the plates.
(a) How many different license plate numbers are available under the current structure of exactly six characters per plate? Show your work.
(b) If the state required all license plates to have exactly seven characters instead of six, how many different license plate numbers would be available with the additional character requirement? Show your work.
(c) How many times bigger is the set of license plate numbers with exactly seven characters than that with the set of six characters? Show your work.
Answer:
9514 1404 393
Answer:
a) 1,544,804,416
b) 52,523,350,144
c) 34
Step-by-step explanation:
(a) Each character position can be any of 24 letters or 10 digits, so any of 34 characters. The number of possible characters sets increases by a factor of 34 for each added character. A six-character plate will have ...
34^6 = 1,544,804,416 . . . possibilities
__
(b) 34^7 = 52,523,350,144 . . . possibilities
__
(c) 34^7/34^6 = 34 . . . times as many
If the volume of a sphere is 36pi cubic units, what is the radius?
- 4 square root 3 units
- 9 units
- 3 units
Answer:
3 units
Step-by-step explanation:
I'm not sure how to explain it but I hope it helps.
Trei stilouri și patru creioane costă 35 lei, iar cinci stilouri și două creioane costă 49 lei. Ce rest va primi Maria de la 100 lei , dacă va cumpăra 4 stilouri și 5 creioane?
Answer:
english?
Step-by-step explanation:
What is the decimal equivalent of 15/8
Answer:
1.875
Step-by-step explanation:
to find the decimal equivalent, you have to divide 15 by 8 which would get you 1.875
Given the following arithmetic sequence find the formula.
Answer:
D. an = 4n
Step-by-step explanation:
The formula for finding a term of an arithmetic sequence is:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term and d is the common difference between the terms.
To find d we can take any two adjacent terms and subtract one from the other. e.g. 8 - 4 = 4, 16-12 = 4 etc.
The common difference here is 4, and we can see that the first term of the sequence is also 4, therefore our formula now looks like this:
an = 4 + (n-1)4
Now we can just expand out the brackets to find the final answer:
an = 4 + 4n - 4
an = 4n
Hope this helped!
HELP!!!!A fish tank that is shaped like a rectangular prism holds 5600cm3 of water. When it is ¾ of the way full, Mike drops 25 identical stones into the water. 180 cm3 of water spill from the tank. What is the volume of each stone?
Answer: 63.2 cm³
Step-by-step explanation:
The tank was 3/4 filled up when the stones were dropped in. This means that the stones had to first get the water level to 4/4 before it could begin to spill. Then after it spilled, it still spilled 180 cm³ of water.
This means that the stones took 1/4 of the total prism and then 180 cm³ as well.
The volume of the 25 identical stones is therefore:
= (5,600 * 1/4) + 180
= 1,580 cm³
The volume of each individual stone is:
= 1,580 / 25
= 63.2 cm³
If x = 3 and y = -4, evaluate:2x2 – 5xy + y
Remember to show your work separately to be submitted in dropbox.
Answer:
[tex]74[/tex]
Step-by-step explanation:
[tex]2 {x}^{2} - 5xy + y \\ 2 \times {3}^{2} - 5 \times 3 \times - 4 + ( - 4) \\ 2 \times 9 - 15 \times - 4 - 4 \\ 18 + 60 - 4 \\ 78 - 4 \\ = 74[/tex]
Hope this helps you.
Can I have the brainliest please?
have a nice day!
Answer:
74
Step-by-step explanation:
2x² - 5xy + y
Substitute x and y into the equation.
2(3)² - 5(3)(-4) + (-4)
Square the three.
2(9) - 5(3)(-4) + (-4)
Multiply the 2 and the 9.
18 - 5(3)(-4) + (-4)
Multiply 3 and -4.
18 - 5(-12) + (-4)
Multiply -5 and -12.
18 + 60 + (-4)
Add 18 and 60.
78 + (-4)
or
78 - 4
Subtract
74
Bella wants to buy blueberries and raspberries to make a fruit tart. Blueberries cost $3.75 per pound and raspberries cost $2.75 per pound. How much does she spend if she buys 3 pounds of blueberries and 1.5 pounds of raspberries? How much does she spend if she buys xx pounds of blueberries and yy pounds of raspberries?
Answer:
a) 15.375
B) at a minimum 65 dollars
Step-by-step explanation:
part one you multiply the pound by the price and get your answer and part 2 its a double digit number so you find the minimum
Probability samples are advantageous to the researcher because: A. they are perfectly representative of the population from which they are drawn. B. the method by which they are selected limits conscious and unconscious sampling bias. C. the method by which they are selected limits conscious and unconscious bias and the accuracy/representativeness of the sample can be estimated. D. they allow the researcher maximum exibility in the creation of samples. E. the accuracy/representativeness of the sample can be estimated.
Answer:
C. the method by which they are selected limits conscious and unconscious bias and the accuracy/representativeness of the sample can be estimated.
Step-by-step explanation:
The probability sampling technique allows for each element in the sample to be representative of the population data from which the samples are drawn. This sort of sampling technique helps to randomize and eliminate errors which might creep into measurement. Since the researcher has the knowledge of the population data or distribution, he takes advantage of these in the allocation of samples using the probabilities of each Sample.
Which expression has a value of 12?
F. 4 x 12 = 3 - (18 – 9) X
G. 18+ (9 X 4+ 12) = 3
H. 9• 3 x 12 - 18 - 1
J. 9 + (18 x 4 = 12) - 3
Answer:
H i think hope it helps you
thank you
|a-5|, if a>5
Please help me
Answer:
answer is just a-5
Step-by-step explanation:
its is a-5 without absolute value
HELP ME PLEASE, ILL GIVE BRANILIST FOR THE BEST CLEAR ANSWER :
William has a new puppy that has completely destroyed the carpet in his living room. If he wants to replace the carpet in the room, which is the best measure?
a
surface area
b
area
c
volume
Answer:
C. Area
hope this helped
1. Which expression is equivalent to 8 - 3?
A 1 x 5
B 3-8
C 8-5
ANSWER QUICK PLZZ NO WEBSITE
Answer:
B I am guessing, not that good at english, though
A sector with a central angle measure of \purpleD{175\degree}175°start color #7854ab, 175, degree, end color #7854ab has a radius of \maroonD{12\,\text{cm}}12cmstart color #ca337c, 12, start text, c, m, end text, end color #ca337c.
Answer: [tex]219.94\ cm^2[/tex]
Step-by-step explanation:
Given
The central angle of a sector measures [tex]175^{\circ}[/tex]
The radius of the circle is [tex]r=12\ cm[/tex]
The area of the sector is given by
[tex]\Rightarrow A=\dfrac{\theta }{360^{\circ}}\pi r^2[/tex]
Insert the values
[tex]\Rightarrow A=\dfrac{175^{\circ}}{360^{\circ}}\cdot \pi \times 12^2\\\\\Rightarrow A=219.94\ cm^2[/tex]
WHat is the largest multiple of 5 that is less than 24
Answer:
20
Step-by-step explanation:
5*4=20
5*5=25, but it is bigger than 24.
So the ans is 20