========================================================
Explanation:
Let's complete the square
y = x^2 + 8x
y + 16 = x^2 + 8x + 16 .... adding 16 to both sides
y + 16 = (x+4)^2
y = 1(x+4)^2 - 16
We added 16 to both sides to allow the right hand side to factor into a perfect square.
The last line shown above is in the form y = a(x - h)^2 + k where
a = 1
h = -4
k = -16
Note the positive 'a' value indicates we have a minimum.
The vertex is (h,k) = (-4, -16)
The lowest y value possible is at the vertex.
So the smallest y value is y = -16.
This means the smallest possible value of x^2+8x is -16.
1. An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Answer:
3 and 12
Step-by-step explanation:
3*5=15 and 15-3=12. The product of 3 and 12 is 36.
The integers are 3 and 12.
What is Algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
let the one integer be x.
Another integer = 5x - 3
According to question,
x *(5x-3 ) =36
5x ² -3 x =36
5x² -3 x - 36 = 0
5x² -15 x +12 x - 36 =0
5x( x-3) + 12 ( x -3) =0
(5x +12)( x- 3)=0
x= -12/5 or 3
So, the integers are 3 and 12.
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Mrs. Garcia deposited $2500 into a new bank account. The bank pays 1.5% interest compounded annually on this account. She makes no additional deposits or withdrawals. How much is in her account at the end of 2 years?
Step-by-step explanation pls! :)
Answer:
$2575.5625
Step-by-step explanation:
2500*(1.015)^2
=$2575.5625
PLS GIVE BRAINLIEST
1st Year 2500*1.015=2537.5
2nd Year 2537.5*1.015=2575.5625
X/4-14=9
what is x?
Step-by-step explanation:
x/4=9+14
x/4=23
x=92
iget 92
Which of the following shows (2x + y) 4 (4 is small) In expanded notation?
Answer:
8x+4y
Step-by-step explanation:
so use the distributive property and multiply 4 into (2x+y), so you get
(2x*4) + (y*4) = 8x + 4y
hope this helped
Simplify: -3x2 + 5x -22 + 4x2 - 9x
a. -7x² + 14x - 22
b. x2 - 4x - 22
c. -X2 + 14x - 22
d. 7x2 + 4x - 22
Answer:
B
Step-by-step explanation:
14.) Mr. Lovell was playing cards with his son. In the first round he earned 52
points. In the second round he lost 20 points. How would you write this as
an addition problem?
Answer:
That would be;
+52-20
Step-by-step explanation:
From the first part, he gained/earned 52 points
This is a positive so we have + 52
In the second round , he lost 20
This is a negative so we have - 20
Writing this as an addition problem, it will be;
+52-20
What is the slope between the points (5,-4) and (-3,4)
-1
4
0
1
Answer:
The answer is -1.
Step-by-step explanation:
You have to apply gradient formula :
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
So you will have to substitute the coordinates into the equation. Let (x1,y1) be (-3,4) and (x2,y2) be (5,-4) :
[tex] m = \frac{ - 4 - 4}{5 - ( - 3)} [/tex]
[tex]m = \frac{ - 8}{8} [/tex]
[tex]m = - 1[/tex]
7x – X – 1=4-7x + 21
Answer:
X=2
Step-by-step explanation:
X^2 + 10x = 0
How do I solve for a completed square ?
Answer:
12x=0
Step-by-step explanation:
x=0 because it is
Answer:
x = 0 x = -10
Step-by-step explanation:
First, use the AC method to figure out, what times what equals 0 and what adds up to equal 10, which would be 0 and 10.
Secondly, you would factor it out and be with
(x + 0)(x +10)=0
Third, you would set each one equal to 0
x + 10 = 0 x + 0 = 0
Solve from there to get your two x's
x = 0 and x = -10
At Pages Aplenty book store, the more books you buy, the more books you get! With the special deal, a customer gets 2 free books for every 7 purchased books. Larry purchased 21 books. How many free books did Larry get?
Answer:
6
Step-by-step explanation:A customer gets 2 free books for every 7 purchased books. Larry purchased 21 books, and you need to find how many free books he got. Write a proportion.
2 free books
7 purchased books
=
? free books
21 purchased books
Compare the denominators.
2 free books
7purchased books
=
? free books
21purchased books
To get from 7 to 21, multiply by 3. Multiply the numerator and denominator by 3 to find the number of free books Larry got.
2 free books3
7 purchased books3
=
6free books
21 purchased books
Larry got 6 free books.
Lerry will get 6 free books . Because she gets 2 free books for every 7 purchased books.
What exactly is simplification?Simplifying means making something easier to do or comprehend, as well as making something less difficult.
For every 7 books a consumer buys, they receive 2 free books. Larry bought 21 books.
If the larry bought 21 book.She get 6 book as;
On the purchased of 7 book then on 14 book and then on the 21 book.
The free books did Larry get is found as;
⇒2+2+2
⇒6
Hence Lerry will get 6 free books .
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An investor flips a house, selling it for $88,000. If her profit was 30%, how much did she pay for the house originally? Round to two decimal places.
Answer:
She paid $67692.31 for the house originally.
Step-by-step explanation:
Let the initial cost of the house be [tex]x[/tex] dollars.
Given:
Selling price of the house (S.P) = $88000
Profit made = 30% of 'x' = [tex]0.30x[/tex]
We know that,
Profit = Selling Price - Original price
[tex]0.30x = 88000 - x[/tex]
Adding [tex]x[/tex] on both sides, we get:
[tex]0.30x+x = 88000\\\\1.3x=88000[/tex]
Dividing both sides by 1.3, we get:
[tex]x = 88000/1.3\\\\x = \$ 67692.307[/tex]
Rounding to 2 decimal places, we get:
[tex]x=\$67692.31[/tex]
Therefore, she paid $67692.31 for the house originally.
There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?
Answer:
Small=36
Large=13
Step-by-step explanation:
As given there are 49 dogs signed up
36 are small so the equation is
36+x=49
x=49-36
x=13
So 13 large dogs and 36 small dogs
PLEASEE HELPP WILL BRAINLIST find the output when x = 0
Answer:
output: 8
Step-by-step explanation:
since x=0 y would equal 8 which is the output.
Suppose you are going to graph the data in the table below. What data should be represented on each axis, and what would be the
appropriate increments?
Reporting periods Sales
d out of 2
Flag
an
Jan-Mar., 2010
$100,000
Apr.-Jun., 2010
$55,000
Jul.-Sep., 2010
$45,000
Oct-Dec., 2010
$110,000
Jan. --Mar., 2011
$330,000
Apr.-Jun., 2011
$800,000
Jul.-Sep., 2011
$242,000
Oct-Dec., 2011
$150,000
Answer:
the months would be the x axis and the numbers would be the y axis and the increments could start at 45k and have to go up to 800k don't forget the years with the months
Evaluate this expression.
112.212 - (- 3.25)
Answer:
115.462
Step-by-step explanation:
Answer: 115.462
Step-by-step explanation:
To start, the first thing we can observe is two negative signs, which we know turns into a positive sign.
Therefore, we now have:
112.212 + 3.25
115.462
Hope this helps!
Please help I’ll mark brainliest if u give a small explanation!!!
Answer:
ut is a if you add 5 plus 4 it makes 9 do not add the 8
x-4y= -36 in slope form
If 4j+3=-5. what is j +9?
Answer:
7
Step-by-step explanation:
First, we solve for j in the first equation:
4j+3=-5
4j=-8
j=-2
Now we plug j into j+9:
-2+9=7
So j+9 is 7
Attachment look at it
im scared to tell my parents im gay plz give me motivation
Same here love!! Remember that if the living environment can get dangerous that it's better to stay in the closet, but besides that Good luck!
Mr. Lyons is laying tile for the rectangular floor of a hotel lobby.
The floor will be 38 tiles wide and 112 tiles long. He has a total of 4,400 tiles.
Which explains whether or not he has enough tiles for the entire floor?
Answer:
yes
Step-by-step explanation:
you find the area by multiplying 38 X 112= 4,256
4,400 - 4,256= 144 left over
Which like is the Skew to RQ. (hint not MN)
what is the value of b and c
Answer:
its 7
Step-by-step explanation:
FInd the circumference of a circle with a diameter of 6 yd. Use the value 3.14 for x and do not round your answers
Answer:
C ≈ 18.85yd
Step-by-step explanation:
An arithmetic sequence has a first term of 8 and sixth term of 38. What is the 50th term of this sequence?
Answer:
302
Step-by-step explanation:
Tn=a+(n-1)d
38=8+[6-1)d
38-8=5d
30/5=d
6=d
Tn=a+(n-1)d
8+(50-1)6
=8+(49)6
302
Hurry i need help!!!!!
Answer:
Sorry i would help but the paper is unclear
Step-by-step explanation:
Suppose the local Barons team wins every game they play with a probability of 0.75. What is the probability that the Barons would win a best-of-seven-game series (i.e., they play games until one team has won four game)?
Answer:
The probability is 0.173
Step-by-step explanation:
The probability is of winning is 0.75 = 75/100 = 3/4
This means that the probability of losing is 0.25 = 25/100 = 1/4
So if they are two win 4 games, they will lose three
We can get this probability using the Bernoulli approximation of the binomial theorem
So here, we have
P(X = 4) = 7 C 4 * 0.75^4 * 0.25^3
= 0.173034667969
which is approximately 0.1730
Hailey is going to use a computer at a Internet cafe. The cafe charges $1.50 for every minute using a computer on top of an initial charge of $4. Make a table of values and then write an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the Internet cafe.
Answer:
The equation is C(t) = 1.50t + 4.00 and the data table is below.
Step-by-step explanation:
We are given that a cafe charges $1.50 for every minute that someone uses the internet. The cafe also charges an initial $4 fee to use the internet.
We need to find a function, in terms of t, that will find these values.
We can treat this as a linear equation. If we initially pay $4, this is acquired before we pay the fee every minute. Therefore, this would be our y-intercept at x = 0. Our first coordinate is (0, 4).
Secondly, if we are charged every minute, this would be a recurring payment and therefore we would spend $1.50 after each minute elapses. This gives us our slope: 1.50 or [tex]\frac{3}{2}[/tex].
Therefore, we can set up our function.
C is the total cost and t is the time, in minutes, that internet is used at the cafe. Our equation can be set up as [tex]C(t) = 1.50t + 4.00[/tex].
Now, we can create a table of values for t = 0 to t = 5 to determine what C(t) is at each of these prime intervals.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} a & 0 \\ \cline{1-2} b & 1 \\ \cline{1-2} c & 2 \\ \cline{1-2} d & 3 \\ \cline{1-2} e & 4 \\ \cline{1-2} f & 5 \\ \cline{1-2} \end{array}[/tex]
This is what our table looks like, but we need to fill the C column. Therefore, we can use substitution of our t-values into the equation and solve for C.
[tex]\bullet \ \text{For t = 0,}[/tex]
[tex]C(0) = 1.50(0) + 4\\\\C(0) = 0 + 4\\\\C(0) = 4.00[/tex]
[tex]\bullet \ \text{For t = 1,}[/tex]
[tex]C(1) = 1.50(1) +4\\\\C(1) = 1.50 + 4\\\\C(1) = 5.50[/tex]
[tex]\bullet \ \text{For t = 2,}[/tex]
[tex]C(2) = 1.50(2) + 4\\\\C(2) = 3.00 + 4\\\\C(2) = 7.00[/tex]
[tex]\bullet \ \text{For t = 3,}[/tex]
[tex]C(3) = 1.50(3) + 4\\\\C(3) = 4.50 + 4\\\\C(3) = 8.50[/tex]
[tex]\bullet \ \text{For t = 4,}[/tex]
[tex]C(4) = 1.50(4) + 4\\\\C(4) = 6.00 + 4\\\\C(4) = 10.00[/tex]
[tex]\bullet \ \text{For t = 5,}[/tex]
[tex]C(5) = 1.50(5) + 4\\\\C(5) = 7.50 + 4\\\\C(5) = 11.50[/tex]
Now, we can insert these values into our table.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} 4.00 & 0 \\ \cline{1-2} 5.50 & 1 \\ \cline{1-2} 7.00 & 2 \\ \cline{1-2} 8.50 & 3 \\ \cline{1-2} 10.00 & 4 \\ \cline{1-2} 11.50 & 5 \\ \cline{1-2} \end{array}[/tex]
Therefore, our equation is C(t) = 1.50t + 4.00 and our data table is above.
Solve using standard algorithm 12.2 * 4.
Answer and Step-by-step explanation:
12.2
* 4
____
48.8
4 times 2 is 8.
4 times 2 is 8.
4 times 1 is 4.
Remember to place the decimal.
#teamtrees #WAP (Water And Plant)
Answer:
48.8
Step-by-step explanation:
Justin wants to buy a new pair of Jean's. If the jeans were originally $50.00, but are on sale with a 30% discount, how much will just have to pay for the jeans?
Answer:oyoyoyohkyhiibjgi
Step-by-step explanation:
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