Answer:
solution
x^3+216=0
or,x^3=216
or,x=6
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)
thank you guys for helping me but i still need help -^-
Answer:
x = 25
Step-by-step explanation:
(4x - 17) + 36 + 61 = 180
(4x - 17) + 97 = 180
4x - 17 = 83
4x = 100
x = 25
Have a nice day!
Answer:
x = 25
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
4x - 17 + 61 + 36 = 180
4x + 80 = 180 ( subtract 80 from both sides )
4x = 100 ( divide both sides by 4 )
x = 25
Mohammed is x years old.
Jenny is 7 years older than Mohammed.
Mario is 3 times the age of Mohammed.
The total of their ages is 82.
What are their ages?
Find the volume and round to the nearest hundredths place when necessary.
Answer:
The top looks like a trapezoid and so does the bottom so it's a prism.
lets find the area of the base!
15(base 1) + 7(base2) = 22
22 x 5(height) = 110
110 divided by 2( x 1/2) = 55
Now we multiply by the actual height of the TOTAL prism which is 11.
55 x 11 = 605 cubic feet, is your answer.
Formula for AREA of a trapezoid:
B1(base 1) + B2(base 2) x H(height) x 1/2 (basically just dividing by 2)
Mark got a loan of $77000 which he will complete repayment in
3 years. If the loan is compounded Sem- Annually at 7% per annum, what amount will he repay? (work out?)
Answer:
A = $94652.66
Step-by-step explanation:
Use the compound amount formula A = P(1 + r/n)^(nt), where r is the annual interest rate and n is the number of compounding periods per year.
Here, A = ($77000)(1 + 0.07/2)^(2*3), or
A = $77000(1.035)^6, or
A = $77000(1.229), or
A = $94652.66
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
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
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
The diagram shows two rectangles.
The combined area of both rectangles is
By considering the areas of the two rectangles, find an equation in the form that satisfies .
We know that :
⊕ Area of a Rectangle is given by : Length × Width
Let us calculate the Area of the Rectangle in the Left side of the figure
⇒ Area of Left Rectangle : (x - 3) (x + 2x)
⇒ Area of Left Rectangle : (x - 3) (3x)
⇒ Area of Left Rectangle : 3x² - 9x
Let us calculate the Area of the Rectangle in the right side of the figure
⇒ Area of the Right Rectangle : (x - 1)(x)
⇒ Area of the Right Rectangle : x² - x
Given : Combined area of both rectangles is 50 cm²
⇒ 3x² - 9x + x² - x = 50
⇒ 4x² - 10x = 50
⇒ 2x² - 5x - 25 = 0
Comparing the above equation with ax² + bx + c = 0,
we can notice that :
→ a = 2
→ b = -5
→ c = -25
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
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
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.
puts $700.00 into an account to use for school expenses. The account earns 4% interest,
compounded continuously. How much will be in the account after 7 years?
Answer:
$926.19Step-by-step explanation:
Use formula:
A = Pe^(rt)Given
P = $700r = 4% = 0.04t = 7 yearsFind the amount:
A = 700*e^(0.04*7) = 926.19if the area of a sector is 15pi square cm and the radius is 5cm find the measure of the central angle
Given:
Area of a sector = [tex]15\pi[/tex]
Radius = 5 cm
To find:
The central angle.
Solution:
The area of a sector is:
[tex]A=\dfrac{1}{2}r^2\theta[/tex]
Where, r is the radius and [tex]\theta[/tex] is the central angle in radians.
Putting [tex]A=15\pi, r=5[/tex] in the above formula, we get
[tex]15\pi=\dfrac{1}{2}(5)^2\theta[/tex]
Multiply both sides by 2.
[tex]30\pi=25\theta[/tex]
Divide both sides by 25.
[tex]\dfrac{30\pi}{25}=\theta[/tex]
[tex]\dfrac{6\pi}{5}=\theta[/tex]
Therefore, the central angle in radians is [tex]\theta=\dfrac{6\pi}{5}[/tex].
Please please please pleasepfoodifieiff
Answer:
8 quadrilaterals
Step-by-step explanation:
a quadrilateral is a shape with 4 sides and vertices
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
Can someone help me with section b please and thank you
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.
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
PLEASE HELP ASAP!! will mark!find the zeros of the function. no links
the answer is x=-1 or x= 5
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
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
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?
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.
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!
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]
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
The cost of hiring a plumber is shown by the equation � = 100� + 75, where n is the number of hours
worked, and C is the total cost to hire the plumber. The plumber wants to earn at least $200 per job,
and will work for a maximum of 6 hours for each job.
(a) What is the minimum and maximum number of hours that the plumber will work?
Answer:
The minimum number of hours the plumer can work is 1 hour and 15 minutes and the maximum number of hours is 6.
Step-by-step explanation: