Answer:
36 liters
Step-by-step explanation:
We solve this question using the least common multiple method
Find and list multiples of the liter the blue paint comes in the liters the yellow paint comes in. We find the first common multiple is found. This is the least common multiple.
Multiples of 9:
9, 18, 27, 36, 45, 54
Multiples of 12:
12, 24, 36, 48, 60
Therefore,
LCM(9, 12) = 36
Hence, the smallest amount of each paint color the store must have sold is 36 liters
PlS HELP QUICKLY :One of the roots of the equation x2−bx+c=0 is equal to 5. Find c in terms of b.:
Guys pls help and find what C is equal to.
Answer:First suppose that the roots of the equation
x2−bx+c=0(1)
are real and positive. From the quadratic formula, we see that the roots of (1) are of the form
b±b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2.
For the root or roots to be real, we require that b2−4c≥0, that is, b2≥4c. In order for them to be positive, we require that
b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√>0.
This immediately tells us that b>0, but we can go further. We can rearrange this to get
b>b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√,
which (assuming that b>0) is true if and only if
b2>b2−4c,
since both sides of the inequality are positive so we may square. But then
4c>0.
That is, if the roots are real and positive then b>0 and b2≥4c>0.
Now suppose that b>0 and b2≥4c>0.
Then the roots of (1) are real since b2−4c≥0, and b>0 guarantees that the root b+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√ is positive.
So it remains to show that b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√>0. We have that
4c>0,
so that
b2>b2−4c,
then square rooting shows that
b>b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√,
so the roots of (1) are real and positive, as required.
Approach 2
the curve y equals x squared minus b x plus c showing two positive roots for y equals zero
This is intended to be a proof without words! We have from the diagram that:
If c, b and b2−4c are all positive, there are two real positive roots for x2−bx+c=0 (if b2=4c, we have two real positive equal roots).
If there are two real positive roots for x2−bx+c=0, then c and b are positive and b2−4c is non-negative.
(Why is the distance between the roots b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√?)
Approach 3
When solving problems about the roots of polynomials, it is often useful to find expressions those roots must satisfy and see if this tells us anything new. If α and β denote the roots of the equation, then
x2−bx+c=(x−α)(x−β)=x2−(α+β)x+αβ
and so α+β=b and αβ=c.
We also know that the roots of a quadratic equation are real if and only if the discriminant is non-negative, that is, if and only if b2−4c≥0.
Using these facts, if α and β are both real and positive, then b=α+β>0, c=αβ>0 and b2≥4c, as above.
Conversely, if b>0 and b2≥4c>0, then we know the discriminant is positive and hence both roots are real. We also have that
αβ>0(2)
and
α+β>0.(3)
As α and β are both real, by (2), we know that α and β are either both positive or both negative. However, if α and β were both negative, then (3) could not possibly hold. Hence α and β are both positive, as required.
We now sketch on a graph the region where b>0, c>0 and b2≥4c:
The curve b squared = 4 c as a quadratic with the c-axis vertical and the b-axis horizontal. The region below it is shaded.
The region of the b-c plane for which b>0, c>0 and b2≥4c
Sketch the region of the b-c plane in which the roots of the equation are real and less than 1 in magnitude.
We know that in order for the roots to be real we need b2≥4c as in the first part. We now need to find the region where
−1<b±b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2<1.(4)
We have b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2≤b+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2 so we only need to consider the values for which both
−1<b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2andb+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2<1.
Firstly, we will consider the values for which
b+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√<2.
Rearranging gives
b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√<2−b.
So b<2, as the square root is non-negative, and we can square both sides to get
b2−4c<4−4b+b2,
which we may rearrange to find c>b−1.
We will now consider the values for which
−2<b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√.
Similarly, we can rearrange to get
b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√<b+2.
So b>−2, and we can, as before, square to get
b2−4c<b2+4b+4,
and hence c>−b−1.
To sketch the graph, we start by considering the boundary curves b2=4c, c=b−1 and c=−b−1, and the points at which they intersect. We can see that the two lines only intersect when b=0 and c=−1, and the lines intersect the curve when
b2=4b−4andb2=−4b−4
which rearrange to
(b−2)2=0and(b+2)2=0.
This tells us that each line intersects with the curve in only one place and so these lines must be tangent.
Is there a way we could have deduced this directly from (4)?
What do the lines being tangent signify in terms of our equation x2−bx+c=0?
Is this a representation of a well-known property of these equations?
Sketching the graph then yields the following picture:
The graph with the previous curve and the lines 4 c = 4 b minus 4 and 4 c = minus 4 b - 4. Each line touches the curve once and the two lines intersect at (0, minus 1). The region between the three lines/curves is shaded.
The shaded region is where b2≥4c, c>b−1, c>−b−1 and −2<b<2
We might notice that when we derived the inequalities c>b−1 and c>−b−1, a lot of the work we did was very similar.
We might also notice that the graph above is symmetric about the c axis. Why is this?
Does the graph give us any ideas about how we might deduce one inequality from the other?
Step-by-step explanation:
WILL GIVE 75 POINTS!! will send $2 IN CASHAPP!
Here are recipes for two different banana cakes. Information for the first recipe is shown in the table.
1st Recipe: y = 1.5x
2nd Recipe: y = 7/4x
If you used 4 cups of sugar, how much flour does each recipe need?
a. First: 2 cups, Second: 8 cups
b. First: 7 cups, second: 6 cups
c. First: 4 cups, second: 2 cups
d. First: 6 cups, Second: 7 cups
Step-by-step explanation:
H hvuvuvuvuvuv9yvig kg
Perform the indicated operations:
-1
4
-4
4
-4
-1
6
-7
-4
-7
-4
2R2 + R3 R3
-4
6
2
-4
8
2
6
-4
30
Answer:
Step-by-step explanation:
The solution is, resulting matrix:[tex]\left[\begin{array}{ccc}4&-1&-4\\-4&6&2\\0&8&10\end{array}\right][/tex][tex]\left[\begin{array}{ccc}-7\\-4\\22\end{array}\right][/tex].
What is Matrix?In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns.
here, we have,
given that,
We are given a matrix,
Let A=[tex]\left[\begin{array}{ccc}4&-1&-4\\-4&6&2\\8&-4&6\end{array}\right][/tex]
and B=[tex]\left[\begin{array}{ccc}-7\\-4\\30\end{array}\right][/tex]
We have to find the resulting matrix after performing given row operations
2R2 +R3 ⇒ R3
Apply
we get,
:A=[tex]\left[\begin{array}{ccc}4&-1&-4\\-4&6&2\\0&8&10\end{array}\right][/tex]
and, B=[tex]\left[\begin{array}{ccc}-7\\-4\\22\end{array}\right][/tex]
Hence, resulting matrix
[tex]\left[\begin{array}{ccc}4&-1&-4\\-4&6&2\\0&8&10\end{array}\right][/tex][tex]\left[\begin{array}{ccc}-7\\-4\\22\end{array}\right][/tex]
To learn more on matrix click:
brainly.com/question/30646566
#SPJ7
Solve: -68.1 * 0.8
A) -54.48
B) 68.9
C) 54.48
D) -68.9
Answer:
A) - 54.48
Step-by-step explanation:
Just plug it into the calculator like this; (-68.1) x 0.8, which equals -54.48.
the answer is negative because you multiplied a positive # and a negative #.
Wendell would like to make some chocolate chips cookies. His recipe calls for the use of 1/2 cups of sugar per batch.he has 3 1/4 of sugar in his apartment. Accidentally, drops 1 cup of sugar on the floor. How many whole batches of sugar cookies can he make with the sugar he had leftover
Answer:
He can make 4 batches of sugar cookies.
Step-by-step explanation: 4x1/2=2 and because he lost 1 cup, he only has 2 cups left
Confused and I need help please
Subtract: 3.8 - 2.923. Explain in your own words how you would solve this, in detail, from start to finish.
Answer:
Step-by-step explanation:
3.8-2.923
Change to 3.800 to match the number of digits in the second number. Work from right to left. 3 minus 0 is 7. work our way over until the end. You should get 0.877 for an answer.
x/6+12=(-12). solve for x
Answer:
x=-144
Step-by-step explanation:
[tex]\frac{x}{6} +12=-12[/tex] subtract 12 on both sides
[tex]\frac{x}{6}=-24[/tex] multiply by six
x=-144
pls help find the inequality represented by the graph
Answer:
use the linear equation of a line
equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
now u do the rest
pls answer QUICK PLSSSS
Step-by-step explanation:
1) 13.57
+2.93
With this, we subtract from the back Meaning we add starting from back to forward;
13.57
+2.93
16.50
We have that because when you add 7 and 3 you get 10 so we write the 0 there and add the remaining 1 to the 5 making it 6 and then 6 plus 9 will give you 15 then we write the 5 then we add the remaining 1 to the 3 making it 4 then we add the 4 to the 2 making it 6 after this there is no remainder so we just write the 1.
Leila and Jo are two of the partners in a business. Leila makes $3 in profits for every $4 that Jo makes. If Jo makes $60 profit on the first item they sell, how much profit does Leila make? pls help U_O
Answer:
54
Step-by-step explanation:
hi
Express this ratio in its simplest form.
240cm : 3.6m
4.5/w = 3
what is the W?
Answer:
w=1.5 or w=13.5
Step-by-step explanation:
this is one answer:
multiply w on both sides to leave u with
4.5=3w
divide both sides by 3
[tex]\frac{4.5}{3}=\frac{3w}{3}[/tex]
1.5=w
_____________________
this is the second one if the first one is wrong:
multiply 4.5 on both sides so that the 4.5/w would leave u with just only w alone.
then 3*4.5=13.5
w=13.5
hope dis helps if not then im not dat smart enough ;?
In a certain chemical, the ratio of zinc to copper is 4 to 13. A jar of the chemical contains 286 of copper. How many grams of zinc does it contain?
Answer: It contains 88 g of zinc.
Step-by-step explanation:
Given: The ratio of zinc to copper is 4 to 13.
Ratio can be written as [tex]\dfrac4{13}[/tex]
A jar of the chemical contains 286 g of copper.
Let the quantity of zinc be x.
By using the direct proportion rule:[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
[tex]\dfrac{x}{286}=\dfrac{4}{13}\\\\ x=\dfrac{286\times4}{13}\\\\\Rightarrow\ x=88[/tex]
Hence, It contains 88 g of zinc.
‼️Help please‼️
A tank full of water is leaking at a constant rate for 30 minutes. The equation y= -7x + 300 gives the amount of water in the tank, where y is the number of liters and x is the number of minutes since the tank began to leak. Which statement is true?
Answer: A
The answer should be A. you probably answered the questoion alr so sorry if you got it wrong
Step-by-step explanation:
it should be A because its not C and D, and B doesnt make sense because it never mentioned anything about 20 minutes.
The garden itself is 5 yards by 8 yards. The total area need to build this landscape
design is 60.9525 square yards. What is the width of the walkway?
O a) 0.725 yards
b) 2.9 yards
C) 1.45 yards
d) 4.58 yards
Answer: 1.45
Step-by-step explanation:
help i’m timed pllzzzzz
Answer:
[tex]a = p*q\\b = (p*s)+(q*r)\\c = r*s[/tex]
Step-by-step explanation:
The standard form of trinomial is given as:
[tex]ax^2+bx+c[/tex]
And the factored form is:
[tex](px+r)(qx+s)[/tex]
In order to find the values of a,b and c in terms of p,q,r and s we will take the factored form, multiply it and then compare it with the standard form.
So,
[tex](px+r)(qx+s)\\=px(qx+s)+r(qx+s)\\= pqx^2+psx+qrx+rs\\= pqx^2+(ps+qr)x+rs[/tex]
Now comparing it with the standard form of trinomial
We will compare the co-efficients of x^2, x and the constant
By comparing, we get
[tex]a = pq = p*q\\b = ps+qr = (p*s)+(q*r)\\c = rs = r*s[/tex]
Hence,
[tex]a = p*q\\b = (p*s)+(q*r)\\c = r*s[/tex]
If 7^9/7^n = 7^3, then n is___.
12
01
-3
3
Answer: 6, but it isn't in your answer choices
Step-by-step explanation: When dividing exponents with the same base, subtract the bottom exponent from the top. In this case, you get 3 from subtracting n from 9, so n should be 6
If a = -9 and b = 4, what is the value of a + b ?
A. -5
B. 5
C. -13
D. 13
Answer:
A. -5
Step-by-step explanation:
-9 + 4 = -5
hope this helps
Tell me a fun fact about horses will give BRAINLIEST to whoever tells me something I don’t know (I have been riding for 12 years) so I know a lot of things (also don’t tell me they can sleep standing up I already know that it’s kinda obvious)
Here are a few fun facts:
A 19th century horse named 'Old Billy' is said to have lived 62 years.
Horses can sleep both lying down and standing up.
Horses can run shortly after birth.
Horses have around 205 bones in their skeleton.
Horses have been domesticated for over 5000 years.
Horses use their ears, eyes and nostrils to express their mood.
Because horse’s eyes are on the side of their head they are capable of seeing nearly 360 degrees at one time.
The fastest recorded sprinting speed of a horse was 88 kph (55 mph). Most gallop at around 44 kph or 27 mph.
The Przewalski’s horse is the only truly wild horse species still in existence. The only wild population is in Mongolia. There are however numerous populations across the world of feral horses e.g. mustangs in North America.
I hope you learned something new!
plz help
Simplify:
- 1.2+15.45
Answer:
- 1.2+15.45=14.43
Step-by-step explanation:
Help please ASAP Thank you
Answer:
uh is it 2 and o.6 i think
Step-by-step explanation:
PLEASE HELP !! BRAINLIEST AND 10 POINTS
My grandfather is shrinking. He decreases in size 1/4 cm each year. What is his total change in height over 5 years. Write your answer using negative numbers
Answer:
That old mans change in height is -1 1/4 over 5 years.
Step-by-step explanation:
Answer:
-5/4 cm would be the answer.
Step-by-step explanation
This is the answer because -1/4 cm multiplied by 5 years would equal -5/4 cm.
What is the initial cost of the car?
Mary is buying hair clips online. The online store charges a fee for each hairclip and a shipping fee. On Monday, Mary placed an order for 8 hairclips, and her total came to $33.75. On Friday, she placed an order for 11 hair clips, and her order came to $44.25. Find the price of each hair clip and the price of shipping.
-10-2r=-3r-7+r how many solutions does this equation have will mark brainlest
Answer:
no solution
Step-by-step explanation:
Choose the correct answer to 8,817/43.
25 R2
205
205 R2
204 R45
Answer:
204 R45
Step-by-step explanation:
Answer: The answer will be 205 R2
Step-by-step explanation:
I know this because the steps to dividing are:
D - Divide
M - Multiply
S - Subtract
B - base(total)
If you do all of those steps then you'll get 205 R2
R = remainder(left overs)
So, the answer will be 205 R2
The function y=2x+6 is shifted down 8 units. What is the equation of the new function?
Answer:
y = 2x -2
Step-by-step explanation:
When you shift down or up, you move down or up the y-axis. Here, the 6 was the y-intercept, so you subtract 8 from 6.
Which graph shows the solution set of the compound inequality 1.5 x minus 1 greater-than 6.5 or 7 x + 3 less-than negative 25?
A number line goes from negative 10 to positive 10. An open circle appears at negative 4 and positive 5. The number line is shaded between the two circles.
A number line goes from negative 10 to positive 10. An open circle appears at negative 4 and positive 5. The number line is shaded from negative 4 toward negative 10. The number line is also shaded from positive 5 toward positive 10.
A number line goes from negative 10 to positive 10. An open circle appears at negative 4. The number line is shaded from negative 4 toward negative 10.
A number line goes from negative 10 to positive 10. An open circle appears at positive 5. The number line is shaded from positive 5 toward positive 10.
Answer:
After solving the compound inequality [tex]1.5x-1>6.5 \ or \ 7x+3<-25[/tex] we get [tex]\mathbf{x>5 \ or \ x<-4}[/tex]
Option B is correct.
Step-by-step explanation:
We are given compound inequality: [tex]1.5x-1>6.5 \ or \ 7x+3<-25[/tex]
We will first solve the inequalities to find the value of x, then will draw the graph.
[tex]1.5x-1>6.5 \ or \ 7x+3<-25\\1.5x-1+1>6.5+1 \ or \ 7x+3-3<-25-3\\1.5x>7.5 \ or \ 7x<-28\\x>\frac{7.5}{1.5} \ or \ x<\frac{-28}{7}\\x>5 \ or \ x< -4[/tex]
So, after solving the compound inequality [tex]1.5x-1>6.5 \ or \ 7x+3<-25[/tex] we get [tex]\mathbf{x>5 \ or \ x<-4}[/tex]
Now, the number line will be as shown in figure.
The description as given in options is:
A number line goes from negative 10 to positive 10. An open circle appears at negative 4 and positive 5. The number line is shaded from negative 4 toward negative 10. The number line is also shaded from positive 5 toward positive 10.
so, Option B is correct.
Answer:
the answer is b
Step-by-step explanation:
2020 edge