Consider the equation:24 = x^2 - 4x + 31) Rewrite the equation by completing the square.Your equation should look like (x + c)^2 = d or (x – c)^2 = d.[ ]2) What are the solutions to the equation?Choose 1 answer:A) x=2 ± 5B) x = -2 ± √5C) x = 2 ± √5D) x = -2 ± √5
Answers
(x - 2)² = 25
Explanation:24 = x² - 4x + 3
rewritting:
x² - 4x = 24 - 3
x² - 4x = 21
using the completing the square:
coefficient of x = -4
square half the coefficient of x = (-4/2)² = (-2)²
Add the square half the cofficient of x to both sides of the equation
x² - 4x + (-2)² = 21 + (-2)²
taking out -4x:
(x - 2)² = 21 + 4
(x - 2)² = 25
The equation above is in the form (x + c)^2 = d or (x – c)^2 = d
Related Questions
I need help with this please
Answers
B.) 0.8415
sofia and manuel are purchasing a home. they wish to save money for 15 years and purchase a house that has a value of $180,000 with cash. if they deposit money into an account paying 5% interest, compounded monthly, how much do they need to deposit each month in order to make the purchase?
Answers
We will have the following:
We will have that the value at the end will be $180 000.
The number of periods will be 15*12 = 180.
The interest per month is 0.05/12 = 0.0042
Now:
[tex]A=\frac{P((1+i)^n-1)}{i}_{}[/tex]Here "A" is the value at the end, "P" will be the monthly payments, "i" the monthly interest rate and "n" the number of periods. So:
[tex]180000=\frac{P((1+0.0042)^{180}-1)}{0.0042}\Rightarrow P=\frac{180000\cdot0.0042}{((1+0.0042)^{180}-1)}[/tex][tex]\Rightarrow P=671.1819761\ldots\Rightarrow P\approx671.2[/tex]So, they will need to deposit approximately $671.2 each month.
Which property of multiplication is shown?
1 · t = t
Answers
The product of 1 and any number is the number
Example:
a x 1 = a
6 x 1 = 6
Hope this helps :-)
22. Which expression is equivalent to
0.71 × 2.8?
A
(B
(71 x 28) x (0.01 × 0.1)
(71 x 28) x (0.1 x 0.1)
(0.71 x 2.8) x (0.01 × 0.1)
D (71 x 28) x (100 × 10)
Answers
Answer: A
Step-by-step explanation:
A (71x28) x (0.01x0.1) = 0.71 x 2.8
B (71 x 28) x (0.1 x 0.1) = 7.1 x 2.8
C (0.71 x 2.8) x (0.01 × 0.1) = 0.0071 x 0.28
D (71 x 28) x (100 × 10) = 7100 x 280
Skate world offers birthday parties for a fee of $130 plus $3 per person. If you can spend no more than $190 on your party. What is the maximum number of people who can attend?
Answers
Answer: 20
Step-by-step explanation:
130+60= 190
60 ÷ 3 = 20
I like kinda need the answer to that : P
Answers
Answer:
its 16
Step-by-step explanation:
Answer:
FG = 16
Step-by-step explanation:
the angle between EF ( y- axis) and EH (x- axis) is right
thus the 4 angles in EFGH are right angles meaning the figure is a square.
the sides of a square are congruent , so
GH = FG , that is
3x + 1 = x + 11 ( subtract x from both sides )
2x + 1 = 11 ( subtract 1 from both sides )
2x = 10 ( divide both sides by 2 )
x = 5
Then
FG = x + 11 = 5 + 11 = 16
PLEASE HELP
y= -2x^2+4x
Direction of opening
Equation of the axis of symmetry (x =___)
Coordinates of the vertex (x,y)
y-intercept (y=_)
Zeroes (if it has 2,1 or no zeroes)
maximum or minimum (y=_)
Answers
AOS: x = 1
Y - intercept: (0 ,0)
Zeros: 0, 2
Maximum
Answer:
see explanation
Step-by-step explanation:
given a quadratic in standard form
y = ax² + bx + c (a ≠ 0 )
• if a > o then curve opens up
• if a < 0 then curve opens down
for y = - 2x² + 4x ← in standard form with a = - 2, b = 4 and c = 0
here a = - 2 < 0 so curve opens down
-------------------------------------------------
the axis of symmetry is a vertical line passing through the vertex
the x- coordinate of the vertex, which is also the equation of the axis of symmetry is
x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{4}{-4}[/tex] = 1
equation of axis of symmetry is x = 1
substitute x = 1 into the equation for y- coordinate of vertex
y = - 2(1)² + 4(1) = - 2 + 4 = 2
vertex = (1, 2 )
-----------------------------------------------------
to find the zeros let y = o , that is
- 2x² + 4x = 0 ← factor out - 2x from each term
- 2x(x - 2) = 0
equate each factor to zero and solve for x
- 2x = 0 ⇒ x = 0
x - 2 = 0 ⇒ x = 2
the zeros are x = 0 and x = 2
-----------------------------------------------------------
since the graph opens down then it has a maximum value
this is the y- coordinate of the vertex
thus maximum at y = 2
I need this answered please
Answers
Carmen invested her saving in fund B as $11,000.
What is termed as the investment?Investing entails allocating capital (money) to tasks or projects that are anticipated to generate a profit over time.The type of return generated is determined by the project or asset; for example, real estate can generate both rents as well as capital gains; numerous stocks pay semiannual dividends; and bonds typically pay regular interest.For the given question;
Let 'x' be the amount invested by Carmen in fund B.
The, the amount invested in fund A is x - 5000.
The profit on fund A is 2% = 2%(x - 5000).
the profit on fund B is 5% = 5%(x).
Then, the total profit is $670.
The equation will be .
2%(x - 5000) + 5%(x) = 670
2(x - 5000)/100 + 5(x)/100 = 670
2x - 10,000 + 5x = 67,000.
Further simplifying.
7x = 67,000 + 10,000
7x = 77,0000
x = 11,000
Thus, amount invested in fund B is $11,000.
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At 11:59 a.m you change the time on your phone to 11:00 a.m. Is the assignment still missing or no?
Answers
Answer:
its still missing
Step-by-step explanation:
U changed it for yourself, not other peoples
Answer: it will say “assigned” but it wouldn’t come up like that for your teacher. I’ve tried it before and it doesn’t work
Step-by-step explanation:
Pre- Calculus
log(x^5)=3
Answers
Answer:
x ≈ 3.9810717
Step-by-step explanation:
the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. after 3 hours it is observed that 400 bacteria are present. after 10 hours 2000 bacteria are present. what was the initial number of bacteria?
Answers
The initial number of bacteria in a culture is found as 200.
What is defined as the population growth?When demographers try to forecast changes in population size, they generally focus on four factors: fertility rates, high mortality (life expectancy), and the population's initial age profile.Using the model P = P₀e^(kt),
Where:
P(t) = the amount of bacteria at time t = 2000.
P₀ = initial amount at time t = 0
r = growth rate
t = time (number of periods)
k is the growth constant.
For t = 3 hours.
400 =P₀e^(k*3) ......eq 1
2000 = P₀e^(k*10) ......eq 2
Re writing eq 1.
400 = P₀e^(k*3)
as (400/P₀) = [e^k]^3,
Solve for e^k,
∛(400/P₀) = e^k
For eq 2.
2000 = P₀e^(k*10)
Rewrite it as;
(2000/P) = [e^k]^10.
Substituting ∛(400/P₀) for e^k, we obtain:
(2000/P₀) = (400/P₀ )^(10/3)
Solved for P.
Raise sides by the power of 3, we get:
(2000/P₀)^3 = (400/P₀)^10.
Therefore,
2000^3/ P₀^3 = 400^10/P₀^10
Solve,
2000^3/ 1 = 400^10/P₀^7
Taking reciprocal.
Solving
P₀^7 = 400^10/2000^3
P₀^7 = 1.31 x 10¹⁶
Take the 7th root of both sides;
P₀ = 200.67
Thus, the initial number of bacteria in a culture is found as 200.
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The figures below are congruent. Name the corresponding sides.
Answers
Answer:
AC=KM
AB=KL
BC=LM
Step-by-step explanation:
Answer:
AC=MK
AB=KL
BC=LM
This are corresponding sides
You have three $1 bills, four $5 bills, and two $10 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. Find P($5 then $10)
1- 1/9
2- 1/12
3- 1/72
4- 2/27
Answers
Answer:
1- 1/9
Step-by-step explanation:
[tex]p(5 then 10) = \frac{4}{9} \times \frac{2}{8} [/tex]
[tex]p(5 then 10) = \frac{1}{9} [/tex]
Assuming without replacement
Evaluate |-15| + |-6|.
Answers
Answer:
21
Step-by-step explanation:
The absolute value of an expression is its distance from 0.
For example, take the number -5:
<-------|------------------|------------->
-5 0
It is 5 units to the left of zero, so its absolute value is 5, NOT -5 because distance is always positive, no matter the direction.
To evaluate the given expression, first find each absolute value:
[tex]|-15| = 15, \, \, \, \, \, \, |-6| = 6[/tex]
Then, simplify:
[tex]|-15| + |-6| \\ =15 + 6 \\= 21[/tex]
So, the evaluated expression is 21.
tell whether 15/35 and 3/7 are proportions
Answers
because
15 / 5 = 3
35 / 5 = 7
Therefore if you divide the numerator and denominator of the first fraction by 5, you will get the second fraction
the chefs at a local pizza chain in cambria, california, strive to maintain the suggested size of their 16-inch pizzas. despite their best efforts, they are unable to make every pizza exactly 16 inches in diameter. the manager has determined that the size of the pizzas is normally distributed with a mean of 16 inches and a standard deviation of 0.8 inch. what are the expected value and the standard error of the sample mean derived from a random sample of 2 pizzas?
Answers
The expected value and the standard error of the sample mean derived from a random sample of 2 pizzas is 0.57
The statistic known as the sample mean is created by arithmetically averaging the values of a variable in a sample.
The sample mean is an estimator of the expected value if the sample is taken from probability distributions with a common expected value.
given
Size of the pizzas 16- inch
normal distribution mean is 16 inch
standard deviation= 0.8
μ=16
σ=0.8
n=2
The standard error of the sample mean derived from a random sample of 2 pizzas is:
σₓ= σ / [tex]\sqrt{n}[/tex]
σₓ = 0.8 /[tex]\sqrt{2}[/tex]
σₓ=0.57
The standard error of the sample mean derived from a random sample of 2 pizzas is 0.57
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Multiple gaming tournaments can be played online. In these games, players can compete with players from any part of the world. Step-by-step-explanation (Simple linear equation)
In a tournament,200 points are awarded for a win, and 20points are deducted for a loss.
Chetan participated in the tournament.
He won two more matches than the number of matches he lost.
He scored 1120 points.
How many matches did he play?
B. 8
A. 6
D. 14
C. 10
Answers
6 x 200 = 1200
4 x 20 = 80
1200 - 80 = 1120
6 + 4 = 10
What is this number in standard form?
(3×100)+(1×110)+(4×11,000)
pls help tysm
Answers
The number (3×100)+(1×110)+(4×11,000) in standard form will be 4.4410 × 10⁴
How to calculate the value?It should be noted that standard form simply means a way of presenting numbers as a mathematical expression.
The number given is illustrated as:
= (3×100)+(1×110)+(4×11,000)
= 300 + 110 + 44000
= 44410
This will be expressed in standard form as:
= 4410
= 4.4410 × 10⁴
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State whether the Law of Detachment, the Law of Syllogism, or the Law of the
Contrapositive was used to draw the conclusion from the given statements. If it's an
invalid conclusion, write invalid.
If you are at least 25 years old, then you can rent a car.
Anna is 28 years old.
Therefore Anna can rent a car.
Law of Detachment
Law of Syllogism
Law of Contrapositive
Invalid Conclusion
Answers
This is an invalid statement. The law of syllogism is what was used to draw the conclusion in the statement here.
What is the law of syllogism?This is the law that is used in logic in the form of
If a , then b . If b , then c . Then we can derive a third true statement: (3) If a , then c.The law of Syllogism can be interpreted as if a person is at least at the age of 25 then they rae able to rent a car. Now given that Anna has fulfilled this condition because she is at the age of 28, then she would be able to rent a car.
Therefore the second option ios correct
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Solve three fifths times v plus 3 equals two fifths times v minus 4. v = −35 v = 35 v equals negative seven fifths v equals seven fifths
Answers
The solution of the expression (3/5)v + 3 = (2/5)v - 4 would be v = - 35 which is the correct answer would be option (A).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
We have to determine the solution of three-fifths times v plus 3 equals two-fifths times v minus 4.
Translate the phrase into an algebraic expression:
⇒ (3/5)v + 3 = (2/5)v - 4
Rearrange the likewise terms and apply arithmetic operations,
⇒ (3/5)v - (2/5)v = - 3 - 4
⇒ (1/5)v = - 7
⇒ v = - 7 × 5
⇒ v = - 35
Therefore, the solution of the expression (3/5)v + 3 = (2/5)v - 4 would be v = - 35.
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A plane flew 216 miles from Bristol airport to Leeds Bradford airport. It had an average speed of 162mph and arrived at 18:15. Work out what time the plane left Bristol airport. Give your answer using the 24 hour clock.
Answers
The plane left Bristol airport at 16:55.
This is a problem from time and distance. We can solve this problem by following a few steps.
We have to know the relation between time, speed, and distance. The relation is denoted as,
t = s/v; t is denoted as time interval, v is denoted as velocity or speed in this case and s is denoted as displacement or distance.
We have to find the time. Here velocity is 162 mph and the total distance between Bristol airport to Leeds Bradford airport is 216 miles.
t = 216 miles/ 162 mph = 1.33 hour = 80 minutes.
Therefore the plane left Bristol airport is, ( 18 hours 15 minutes - 80 minutes) = 16 hour 55 minutes = 16:55
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a town's population has been growing linearly. in 2003, the population was 59000, and the population has been growing by 1700 people each year. write an equation for the population x years after 2003.
Answers
Answer:
The population after x years will be P = 29000 + 700x
Let the population after the years be represented by P
Population of the town in 2003 = 29000
Annual increase in growth = 700
Then, the population after x years will be:
P = 29000 + 700(x)
P = 29000 + 700x
Therefore, the population will be P = 29000 + 700x.
Bette used 3 jumbo cans of frosting to frost 105
cupcakes for the cupcake challenge at her school
and 5 jumbo cans of frosting to frost an
additional 175 cupcakes. How many jumbo cans
of frosting would she need to frost 280
cupcakes?
Answers
Bette needs 8 jumbo cans of frosting to frost 280 cupcakes.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Bette used 3 jumbo cans of frosting to frost 105 cupcakes for the cupcake challenge at her school and 5 jumbo cans of frosting to frost an additional 175 cupcakes which are given in the question.
Let x jumbo cans of frosting would she need to frost 280 cupcakes
As per the given question, we can write the ratio as
3 jumbo cans of frosting : 105 cupcakes = x jumbo cans of frosting : 280 cupcakes
⇒ 3/105 = x/280
⇒ x = ( 280 × 3 )/ 105
⇒ x = 8
Therefore, she needs 8 jumbo cans of frosting to frost 280 cupcakes.
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the slop of (4,10) and (6,9)
Answers
Answer: [tex]\frac{1}{-2}[/tex]
Step-by-step explanation:
Slope =
[tex]\frac{Y2-Y1}{X2-X1}[/tex]
[tex]\frac{10-9}{4-6}[/tex]
[tex]\frac{1}{-2}[/tex]
The stopwatch shows the time Mike took to complete a puzzle.
Round this time to 1 d.p.
36.98sec
Answers
Answer:
37.0seconds
Step-by-step explanation:
when you round you take the second number (8) and find out if it is higher or lower than 5. When it is higher you round up.
But, since the next number is 9 you have to continue to round up the next number which is 6.
Hope this is helpful!
A family arrives at the Walt Disney world parking lot to get from their car in the parking lot to the gate at the magic kingdom they walk 1/4 mile take a train for 1/3 of their total distance and take a monorail for 1/2 of their total distance how far is it from their car to the gate of magic kingdom
Answers
This is equivalent to 3/2 as an improper fraction and 1 & 1/2 as a mixed number.
==========================================================
Explanation:
x = total distance in miles
The train and monorail take 1/3 and 1/2 of the total distance respectively
Add up those fractions to get
1/3 + 1/2 = 2/6 + 3/6 = 5/6
Remember that you can only add fractions when the denominators are the same.
5/6 of the total distance consists of the train and monorail.
That means the walking portion must be 1 - 5/6 = 6/6 - 5/6 = 1/6 of the total distance.
----------------------------
In short, we found that 1/6 of the total distance consists of walking.
(1/6)x = 1/4 mile
x/6 = 1/4
4x = 6*1
4x = 6
x = 6/4
x = 3/2
x = 1.5 miles is the total distance
---------------------------
Check:
1/6 of x = 1/6 of 3/2 = (1/6)*(3/2) = 3/12 = 1/4 mile walking
1/3 of x = (1/3)*(3/2) = 3/6 = 1/2 mile on the train
1/2 of x = (1/2)*(3/2) = 3/4 of a mile on the monorail
1/4 + 1/2 + 3/4 = 1/4 + 2/4 + 3/4 = 6/4 = 3/2 = 1.5 miles total
This confirms our answer.
Please help i havent been turning in my math work for days and im so close to getting detention
Answers
Answer: 1.one cup
2. 2 cups of each
Step-by-step explanation:
Is this a function if so explain if not explain
Answers
Answer:
Not a function
Step-by-step explanation:
It is not a function because it doesn't pass the vertical line test.
Help ASAP Giving 20 Points
Answers
Answer:
10.9 feet
Step-by-step explanation:
its Pythagoras but reversed. So instead of a squared plus b squared equals c squared its (c squared)-(a squared) equals (b squared)
so (12x12) - (5x5) = 119
square root of 119 is 10.9
sorry im replying on phone i cant do exponents and stuff
At a dinner party, each guest is to receive a bag of small gifts. How many gifts should be placed in each bag if there are 8 guests and 32 gifts altogether?
Answers
Answer:
4Step-by-step explanation:
Total number of gifts = Sum of all gifts given to each guest
= (Number of guests) * (Number of gifts per guest)
By making the number of gifts per guest the subject of the formula:
Number of gifts per guest = Total number of gifts/Number of guest
But:
Total number of gifts = 32
Number of guests = 8
Number of gifts per guest = Total number of gifts/Number of guest
=32/8
=4