First write the function [tex]y=(x+12)(x-6)[/tex] in standard form [tex]y=ax^2+bx+c:[/tex]
[tex]y=x^2-6x+12x-72,\\\\y=x^2+6x-72.[/tex]
Find the x-coordinate according to the rule
[tex]x_{vertex}=-\dfrac{b}{2a}.[/tex]
Thus,
[tex]x_{vertex}=-\dfrac{6}{2\cdot 1}=-3.[/tex]
Now find the y-coordinate of the vertex substituting x=-3 into the parabola equation:
[tex]y_{vertex}=(-3)^2+6\cdot (-3)-72=9-18-72=-81.[/tex]
Answer: the x-coordinate if the vertex is -3.
The x-coordinate of the parabola’s vertex is 3
How to determine the x-coordinate of the parabola’s vertex?from the question, we have the following parameters that can be used in our computation:
y = (x - 6)(x + 12)
When expanded, we have
y = x² - 6x + 12x - 72
So, we have
y = x² + 6x - 72
the x-coordinate of the parabola’s vertex is calculated as
x = -b/2a
So, we have
x = -6/2* 1
Evaluate
x = -3
Hence, the x-coordinate of the parabola’s vertex is 3
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What is the value of x?
3(x−2)+5x=18
X = ????
3(x-2)+5x=18
the correct answer is x=3
first simply the equation
8x=18+6
Now rid of alike terms resulting in
8x=24
now divide 24 by 8
x=3
Complete each number pattern
8,625 8,725 ______ ______ 9,024
862 962 _____ 1,162 ______
6,215 _____ 6,015 _______ ______
What does |-2 + (-1)| equal too
[tex]|-2 + (-1)|[/tex]
Well, first, we must subtract-2 by 1, as the negative sign next to 1 is inside the parentheses.
[tex]|-2 -1|[/tex]
[tex]|-3|[/tex]
Now remember, since it is an absolute value, meaning the distance from that number to zero, we will now disregard the negative sign and get our answer: 3
Solve -3 1/2 = 1/2x + 1/2x + x
- 3 1/2 = 2x
-7 /2 = 2 x
-7 /4 = x
-1 3/4 = x
what is the m<PHJ
A. 100°
B. 120°
C. 140°
D. 160°
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
∠PML = 140°
∠KHP = 20°
We need to find the measure of ∠PHJ.
Let m ∠PHJ = x°
From the graph, we conclude that
∠PML = ∠PHJ + ∠KHP (Vertically opposite angle)
[tex]140^\circ=x+20^\circ\\\\140^\circ-20^\circ=x\\\\120^\circ=x[/tex]
Hence, Option 'B' is correct.
if 75 is added to a number, the result is 39 less than three times the number.find the number
First, we would set the number to x.
Then, we turn the words into an equation.
x+75 = 3x-39
Isolate the x.
-2x = -114
So...
x = 57
The Number is 57.
Let's call the number you're trying to find "x."
According to the information given, if 75 is added to x, the result is 39 less than three times the number, which can be expressed as:
x + 75 = 3x - 39
To solve for x, you can first get all the x terms on one side of the equation and the constant terms on the other side:
75 + 39 = 3x - x
Now, simplify the equation:
114 = 2x
To isolate x, divide both sides by 2:
x = 114 / 2
x = 57
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Nina earns $15 for each yard she mowes. she wants to buy a dress that coasts $109. how many yards will she need to mow to earn money for the dress? explain
she will need to mow 8 yards because 109 divided by 15 equals 7.2 but she cant just mow 7.2 yards so you round up to 8 yards
Holly
has 25 fish in her aquarium. Tommy has one-fifth the number of fish that Holly has. Jared has three times as many fish as Tommy. If they combine all their fish in the new school aquarium, how many fish would there be in all?
find the slope of the line
the slope is 3/-5!!!! if u go up 3 and to the LEFT 5 that means it is negative.
Brandon enters bike races he bikes 8 and 1/2 miles every 1/2 hour complete the table to find how far Brandon bikes for each time he interval else if he likes 8 and 1/2 Mile for 1/2 hour how many miles does he bike per 1 hour
We find he bikes 17 miles in a full hour.
Brandon bikes 8 and 1/2 miles in 1/2 hour. To find out how far he bikes in 1 hour, we need to double the distance, because one hour is twice as long as half an hour.
Miles per hour = Miles in half an hour * 2 = (8 + 1/2) miles * 2
Now, let's perform the multiplication:
8 * 2 = 16
1/2 * 2 = 1
Therefore, 16 + 1 = 17 miles per hour.
Brandon bikes 17 miles in 1 hour. This is the distance he would cover if he continues at the same pace for a full hour.
10p-2(3p-6)=4(3p-6)-8p please show work
A yogurt shop allows its customers to add, for no charge, 3 toppings to any yogurt purchased. If the store has 15 possible toppings, how many different 3-topping combinations can a customers choose?
Question says that a yogurt shop allows its customers to add, for no charge, 3 toppings to any yogurt purchased. Also the store has 15 possible toppings.
Now we need to find about how many different 3-topping combinations can a customers choose.
To find that we just need to apply combination formula
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
which is used to select r items out of n items
we have to find combination of 15 toppings into 3 toppings so we calculate C(15,3) using above formula
[tex]C(15,3)=\frac{15!}{3!(15-3)!}[/tex]
[tex]C(15,3)=\frac{15!}{3!*12!}[/tex]
[tex]C(15,3)=\frac{15*14*13*12!}{3!*12!}[/tex]
[tex]C(15,3)=\frac{15*14*13}{3!}[/tex]
[tex]C(15,3)=\frac{2730}{6}[/tex]
[tex]C(15,3)=455[/tex]
Hence final answer is 455.
Answer:
only 455
Step-by-step explanation:
i have a ? how do you know when its C(n,r) and not P(n,r)
Heres the problems I need help with....asked this earlier to get answers that were apparently incorrect..this is about repeating decimals.
When changing a repeating decimal to a fraction, you look at the number(s) to the right of the decimal. If there is only 1 number (0.444444...) then the number that repeats is is going to be the numerator of your fraction, with the denominator being 9 (4/9). So...
1. -1 2/9 (-1 and 2/9)
2. -5/9
5. 5 8/9 (5 and 8/9)
If there are 2 or more numbers to the right of the decimal, you add 1 "9" to the denominator per repeating number (2 repeating numbers = 99, 3 repeating numbers = 999, etc...). An example to show this would be 0.87 repeating (0.87878787... = 87/99). Therefore...
3. 27/99
4. 50/99
I hope this helps!
one number is three less than four times another. if their sum is decreased by seven, the result is twenty. find the numbers
x = 21
y = 6
x = 4y - 3
x + y - 7 = 20
Because we have a value for x, we can put it in the second equation to find the value of y.
4y - 3 + y - 7 = 20
Combine like terms.
5y - 10 = 20
Add 10 to both sides.
5y = 30
Divide both sides by 5.
y = 6
Now we can place this value of y back into the equation to find the exact value of x.
x + 6 - 7 = 20
Combine like terms.
x - 1 = 20
Add 1 to both sides.
x = 21
The graphs below show the number of honor roll students in each grade at Bridgeport Middle School. Which statement is true??
A. According to Graph 2, there are more than twice as many sixth graders on the honor roll than eighth graders on the honor roll.
B. The scale on Graph 1 does not distort the differences in the number of students.
C. The two graphs use completely different data
D.both: “according to Graph 2, there are more than twice as many sixth graders on the honor roll than eighth graders on the honor roll” and “the two graphs use completely different data”
The top of a refrigerator has an area of 0.6 m^2. The height of the refrigerator is 180 CM. What volume does the refrigerator occupy in CUBIC METERS?
Note: all measurements of the refrigerator need to be in meters, make sure you have IDENTICAL units.
SHOW WORK PLEASE
THANKS IN ADVANCE! :)
the volume (V ) of a cuboid is V = Ah
where A is the area of the base or top and h is the height
h = 180 cm = 1.8m
V = 0.6 × 1.8 = 1.08 m³
The volume of the refrigerator is calculated by converting its height from centimeters to meters (180 cm = 1.8 m) and then multiplying it by the given area of the top (0.6 m²), resulting in a volume of 1.08 cubic meters.
To calculate the volume of the refrigerator, we need to use the formula for the volume of a rectangular prism, which is Volume = length x width x height. We already have the area of the top of the refrigerator, which is a product of its length and width, and we're given the height. However, firstly we need to ensure that all units are in meters.
Convert the height from centimeters to meters: 180 cm = 1.8 m.
Now, we can calculate the volume: Volume = Area x Height = 0.6 m² x 1.8 m = 1.08 m³.
Therefore, the refrigerator has a volume of 1.08 cubic meters.
Mr. Glidden is expanding the size of his garden. His new garden will be 3 times as long and 2 times as wide as his original garden. The perimeter of his original garden is 30 feet and the length is 11 feet. What will be the perimeter, in feet of his new garden?
Method One:
Step One: Figure out how long the width is, witch is 19 feet.
Step Two: Multiply 2*19 and 3*11 because it is 2 times as long and three times as wide
Step Three: Add 38+33
The new perimeter will be 71 feet.
The original garden's width is determined to be 4 feet. Upon expanding the garden to triple its length and double its width, the new garden's perimeter is calculated to be 82 feet.
The question is about calculating the perimeter of a new garden based on given dimensions and scale factors for its expansion. The original garden has a perimeter of 30 feet and a length of 11 feet. To find the width, we use the formula for the perimeter of a rectangle, P = 2l + 2w, which gives us 30 = 2(11) + 2w. Solving for w, we find that the width of the original garden is 4 feet.
Given that Mr. Glidden is expanding his garden to be 3 times as long and 2 times as wide, the new dimensions will be 3(11) feet by 2(4) feet, or 33 feet by 8 feet.
Therefore, the new perimeter will be 2(33) + 2(8), which equals 66 + 16, resulting in a new perimeter of 82 feet.
Nikita invest 2000 into a bank account with a 4% annual interest rate. In seven years which is the most expensive item she can afford to buy
a) 2,700.
B) 2,500
c) 2,200
D) 3,000
Answer:
The correct option will be: B) 2,500
Step-by-step explanation:
Nikita invest 2000 into a bank account with a 4% annual interest rate.
So, the amount of interest in one year will be: [tex](2000*0.04)= 80[/tex]
and the amount of interest in 7 years will be: [tex](80*7)=560[/tex]
Thus, the total money in her account after 7 years [tex]=(2000+560)=2560[/tex]
So, the most expensive item she can afford to buy will be: 2500
Answer:
The answer is (a mountain bike priced at $2,500) In Plato
Step-by-step explanation:
HELP ME PLEASE THANKS SO MUCH !
The answer is C,
200 is the original distance
plus the increasing 5 yards everyday
Help algebra 2 questions.
For the first question, divide 200 by the seconds. You would get the answer 9.07. This answer is rounded to the nearest hundredth.
The second question, you would convert that to feet by using the units 1 meter = 3.28084.
If you converted it, the answer woudl be 29.75722 ft/second
Rubin has 6 rolls of pennies containing 50 coins each, 5 rolls of nickels containing 40 coins each, 4 rolls of dimes containing 50 coins each l, and 3 rolls of quarters containing 40 coins each. How much money does he have?
6•50=$3.00 pennies
5•40=$2.00 nickels
50•10=$5.00 dimes
25•40=$10.00 total $20.00
Answer: $63
Step-by-step explanation:
Penny = $0.01
Nickel = $0.05
Dime = $0.1
Quarter= $0.25
Number of pennies = 6(50) = 300
Number of nickels = 5(40)= 200
Number of dimes = 4(50)= 200
Number of quarters = 3(40) = 120
Total amount of money:
300(0.01)+ 200(0.05) + 200(0.1) + 120(0.25) = $63
When the absolute value of the slope gets smaller, the graph of a line gets
_______.could you use?
a. shorter
b.steeper
c.longer
d.less steep
The graph of the line would get less steep.
(APEX approved~)
Answer:
D) Less steep.
the volume of a rectangular prism can be found by multiplying the length width and height of the prism which of the following following could be possible dimensions of a rectangular prism that has a volume of 75 ft
D
because 3*5=15 And 15*5=75
Miguel babysits for 3 hours and earns $15. Which represents the unit rate?
The unit rate is $/Hr. Since the hours are the unit being considered.
To find the unit rate, divide both sides by three
(Let x = hourly rate)
3x = 15
x = 5
Miguel Makes $5 per Hour
Answer:
He Earns 5 Per Hour
The amount a babysitter earns is given by the equation y=7.5x where x is the number of hours and y is the amount earned in dollars. Is this relationship proportional?
Yes, this relationship is proportional.
Answer:
Yes, the relationship is proportional
Step-by-step explanation:
This is because the number of hours (x) is multiplied by the same number, 7.5, meaning that all of the values will be proportional (create a straight/linear line on a graph when the points are plotted).
What is x > -3 as an interval notion?
(- 3, ∞ )
the parenthesis at both ends indicates x ≠ - 3 or ∞
if x ≥ - 3 then {- 3, ∞ )
the square bracket on the left indicates x can equal - 3
Final answer:
The inequality x > -3 in interval notation is (-3, ∞), which means that the solution set for x includes all values greater than -3, but does not include -3 itself.
Explanation:
When the inequality x > -3 is written in interval notation, it means that the solution set for x includes all values greater than -3, but does not include -3 itself. In interval notation, we use a round bracket to indicate that -3 is not included in the solution set. The interval notation for x > -3 is (-3, ∞). This notation represents a half-open interval, where -3 is excluded but all values greater than -3 are included. The symbol ∞ represents infinity, indicating that there is no upper bound for the values of x in this inequality.
Solving an equation like this
3x-4=18+5x
What is the standard form of the number shown in this calculator display?
3.82e+7
38.9e i think 60% sure
Ryan drives his car on a trip and goes 4,000Km , how many miles did he travel? (1 miles=1.609 km )
2,486.016 miles of distance Ryan drives his car on a trip.
Given that, Ryan drives his car on a trip and goes 4,000 km.
We need to find how many miles he travels.
How to convert kilometres to miles?1 kilometre is equal to 0.621371 miles (often shortened to .62) and 1 mile is equal to 1.609344 kilometres. Thus, to convert kilometres to miles, simply multiply the number of kilometres by 0.62137.
Now, divide the number of kilometres by 1.609
That is, 4000/1.609=2,486.016 miles
Therefore, 2,486.016 miles of distance Ryan drives his car on a trip.
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whats the answer of the problem peter is 3 years older than his sister Anna. if times their combined age is 85 . determine Annas age
Answer:
Anna is 41 years old.
Step-by-step explanation:
Easiest way to do this is by building a equation,
Lest say Anna's age is [tex]x[/tex].
Then as Peter is 3 years older than Anna Peter's age should be [tex]x+3[/tex].
Then the combined ages of the two people is given as 85. So we can write an equation as,
[tex]x+(x+3)=85[/tex]
[tex]x+x+3=85[/tex]
[tex]2x+3=85[/tex]
[tex]2x+3-3=85-3[/tex] (deducting 3 from both sides of the equation)
[tex]2x=82[/tex]
[tex]x=41[/tex]
As we originally took Anna;s age as [tex]x[/tex]
We can say Anna is 41 years old.