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Work Shown:
a:b = 1:3
a/b = 1/3
a*3 = b*1 ... cross multiply
3a = b
b = 3a
Since b is a one digit number, this means that the largest it can get is 9
[tex]b \le 9\\\\3a \le 9\\\\a \le \frac{9}{3}\\\\a \le 3[/tex]
The largest possible value of 'a' is 3
QUADRATIC EQUATION – WORD PROBLEMS
Fatima got 16 marks more than Zahra in Math test. The product of their mark is 1380. Find their marks.
The answer 30 ,46
I just need the steps
Answer:
Fatima's points = 46
Zahra's points = 30
Step-by-step explanation:
Let's give names to the unknowns (the number of points each one got)
Fatima's points = y
Zahra's points = x
Now create the equations given by the info they provide:
"Fatima got 16 marks more than Zahra"
y = x + 16
"The product of their mark is 1380."
x * y = 1380
Now use the first equation as substitution for "y" in the second equation:
x * (x + 16) = 1380
reduce the expression:
x^2 + 16 x = 1380
x^2 + 16 x - 1380= 0
Solve using quadratic formula:
[tex]x=\frac{-16+/- \sqrt{16^2+4(1380)} }{2} \\x=\frac{-16+/- \sqrt{5776} }{2} \\x=-8+/- 38\\x = 30\,\,\,or\,\,\,x=-46[/tex]
we pick 30 since the scores from a test must be larger than zero.
Now we use the first equation to solve for the other variable;
y = 30 + 16 = 46
then x = 30 and y = 46
Suppose we write down the smallest positive 2-digit, 3-digit, and 4-digit multiples of 9. what is the sum of these three numbers?
Answer: 1134
Step-by-step explanation:
What is 8/9 - 1/18? Please put in fraction form.
:)
Answer:
5/6
Step-by-step explanation:
8/9=16/18
16/18-1/18=15/18
15/18 divided by 3 is 5/6
Answer:
5/6
Step-by-step explanation:
Please answer asap
Use the graph to determine the input value for which f(x) = g(x) is true.
x = 0.5
x = 1
x = 1.5
x = 2
What is 3/4 of a dollar forgot will mark Brainliest if right
Answer:
0.75 U.S. dollars
Step-by-step explanation:
If you're talking U.S dollar. It's 0.75 cents.
This doesn't seem like college work.
PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
D
The reason its D is because π is a irrational and its not a real number. Search it up. Hope i get brainliest!
hope this helped :)
of the 50 students in the cafitera, 7 have red hair. If there are 750 students in the school, predict the number of students who have red hair.
What is the length of the hypotenuse of the triangle?
Answer:
It depends, you have to use the Pythagorean Theorem
explanation:
Answer:
If you have both legs, then you can use the PYTHAGOREAN THEOREM to find the value of the hypotenuse. a^2 + b^2 = c^2 ( a= leg, b = leg, c = hypotenuse)
Step-by-step explanation:
If you do not have a leg value, but you do have an angle measure, then you can use Sine or Cosine to find the hypotenuse. Sin = opposite/hypotenuse and Cos = adjacent/hypotenuse.
Let me know if you need further explaination!
2/3 plus 6 1/5
pls also thank you if you do and you get brainlist
Aaliyah invested $350 in an account paying an interest rate of 4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 20 years?
Answer:779
Step-by-step explanation:
Delta
In the diagram below,Ab and De bisect each other.If f is the midpoint dc, AB=20 and De=12, find the value of FC+CB.Show how you arrived at your answer.
Answer:
13
Step-by-step explanation:
AB = 20
DE =12
Since AB and DE bisect each other, therefore:
AC = CB = ½(AB)
AC = CB = ½(20)
AC = CB = 10
Also,
DC = CE = ½(DE)
DC = CE = ½(12)
DC = CE = 6
Since F is the midpoint of DC, therefore:
FC = ½(DC)
FC = ½(6)
FC = 3
Find the value of FC + CB. Plug in the values of FC and CB:
3 + 10 = 13
Zach's baseball team is raising money for a charity. Zach is tasked with raising at least $250. If represents the amount of money Zach raises, which inequality represents this situation?
a. x>250
b. x<_250
c. x>_250
d. x<250
Answer: x ≥ 250
Step-by-step explanation:
Maggie's brother is 4 years younger than three times her age. The sum of their ages is 16.
How old is Maggie?
Answer:
Maggie is 5 years old
Step-by-step explanation:
3M-4+M=16
add 4 to both sides
4M=20
Divide both sides by 4
20/4 = 5
M/Maggie is 5
What is 1 and 3 quarters multiplied by 4 and 1 sixth
1_3/4 • 4_1/6
(7/4) (25/6) = 175/24
Answer: 175/24
Two angles of a triangle measure 53. What is the measure of an exterior angle at each vertex of the triangle?
Answer:
53+53=106
180-106=74
74 + 53= 127 (answer 1)
53+53=106 (answer 2)
74+53=127 9answer 3)
The measure of each exterior angle is 106, 127, and 127 degrees if the two angles of a triangle measure 53.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have:
Two angles of a triangle measure 53:
The measure of the angles of a triangle:
53, 53, (180-53-53)
53, 53, 74 in degrees
As we know,
The sum of the two interior angles of a triangle is equal to the exterior angle:
Exterior angle(1st vertex) = 53 + 53 = 106 degrees
Exterior angle(2nd vertex) = 53 + 74 = 127 degrees
Exterior angle(3rd vertex) = 74 + 53 = 127 degrees
Thus, the measure of each exterior angle is 106, 127, and 127 degrees if the two angles of a triangle measure 53.
Learn more about the triangle here:
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Please help me, if correct get brainliest
Answer:
If I am correct the answer should be graph it !!!! first quadrant
corners
(0,0)
(0,3)
(1.5 , 3.5) intersection
(5,0)
evaluate 6x-4y at those corners
0
-12
-5
+9
makes sense, need big x and small y :)
Step-by-step explanation:
I apologize if I am incorrect I am only in 7th grade but I am pretty intelligent so please try it out!
C) Work out 3/4 × 5 (Give your answer as the simplest mixed fraction).
Answer: 3 ¾
------------------
Answer:
15/4=3 3/4
Step-by-step explanation:
3 and 3/4 is the awnser
You need 660 mL of a 80% alcohol solution. On hand, you have a 40% alcohol mixture. How much of the 40%
alcohol mixture and pure alcohol will you need to obtain the desired solution?
You will need
mL of the 40% solution
and
mL of pure alcohol.
Submit Question
Let a be the amount of 40% solution and b be the amount of pure alcohol that you will use.
You want to end up with a volume of 660 mL, so
a + b = 660
For each mL of solution used, the 40% solution would contribute 0.4 mL of alcohol, and the pure alcohol will contribute 1 mL of alcohol. In the desired solution, you want a concentration of 80% alcohol, so that it contains 0.8 • 660 mL = 528 mL of alcohol, and
0.4a + b = 528
Solve the system of equations above. Subtracting the second from the first eliminates b and lets us solve for a :
(a + b) - (0.4a + b) = 660 - 528
0.6a = 132
a = 220
Then
220 + b = 660
b = 440
So you will need 220 mL of the 40% solution and 440 mL of pure alcohol.
Beth bought 35¢ stamps and 15¢ stamps at the post office. If she purchased 60 stamps at a cost of $17, how many of each kind did she buy?
Answer:
She buys 20 Stamps of $0.15 and 40 Stamps of $0.35.
Step-by-step explanation:
40 x 0.35 = 14
20 x 0.15 = 3
$14 + $3 = $17
40 ($0.35) + 20 (0.15) = 60 stamps
f(x)=x^(2)-4x+32 is it true that it equals (0,32) on the y-intercept
Answer: Yes this equation is true.
How Do I know? Well, let's graph this and the answer is (0,32)
Answer:
Yes, it's true
A girl is swimming 1 meter below sea level and dives down another .5 meters. How far below sea level is she now?
Answer:
1.5 meters
Step-by-step explanation:
If she is already below sea level by 1 meter and she goes down .5 meters more, she would be 1.5 meters below the sea level.
3 + (-4)
1/4 X (-1 1/2 - 1/2)
Answer:
35
Step-by-step explanation:
Someone please help!!!!!!!!!
Answer:
-32
Step-by-step explanation:
Simply input the x and y values.
New equation:
| 147-(-9) | /(-4) +7
Step one:
147-(-9) = 156
Step two:
|156|/-4 =-39
Step three:
-39+7 =-32
If you evaluate the expression it comes out to -32
Vhat is the equation of the line that is parallel to the
given line and passes through the point (2, 3)?
O x + 2y = 4
O x + 2y = 8
O 2x + y = 4
O 2x + y = 8
Step-by-step explanation:
second one because
only x+2y=8 passes through the point (2,3)
the proof is 2+2*3=2+6=8
if we replace the given point to the other equations we will take wrong results for example
first equation
x+2y=4. 2+2*3=2+6=8 that is not equal to 4
Slopes of lines which are parallel to each other is same. The equation of the line which is parallel to y = mx + c and passes through (2,3) point is y = m(x-2) + 3
How are parallel straight lines related?Parallel lines have same slope, since slope is like measure of steepness and since parallel lines are of same steepness, thus, are of same slope.
In the line of the form [tex]y = mx + c[/tex], the coefficient of x, which is 'm' here, is the slope of the line [tex]y = mx + c[/tex]
Suppose that the given line be:
[tex]y = mx + c[/tex]
(we assume this, because the question is a bit incomplete as the initial line isn't given)
And we've to find the equation of a line which is parallel to the line given above, and passes through (2,3).
Suppose it be:
[tex]y = mx + b[/tex] (as the slope of parallel lines would be same).
This line passes through (2,3), so the equation must be true for (x,y) = (2,3).
Putting it, we get:
[tex]y = mx + b\\3 = m(2) + b\\3 - 2m = b[/tex]
Thus, the equation of this line is:
[tex]y = mx + b \\y = mx + (3-2m)\\y = m(x-2) + 3[/tex]
Learn more about parallel lines here:
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NEED HELP ASAP!! which function has a range of y is greater than or equal to 0
Answer:
c
Step-by-step explanation:
The third function has a range of y that is greater than or equal to 0.
What is a function?A function is a kind of rule that, for one input, gives you one output.
For the first function, it contains negative values for y, so it was eliminated.
The second function did not start from zero, so it was eliminated.
The third function obeys the given condition, but the last function contains negative values for y.
Hence, the third function satisfies the condition that y is greater than or equal to 0.
To learn more about function, use the link given below:
https://brainly.com/question/21145944
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At the market, 8 batteries cost $10,
How much do 6 batteries cost?
Answer:
$7.50
Step-by-step explanation:
You can use proportions to find that 8/10 = 6/x
then you can multiply 10 by 6 and divide the result by 8 to get the answer.
You can also divide 10 by 8 to get 1.25 and multiply it by 6, as 10 divided by 8 gives you the unit rate, or the price of each battery. Then you multiply it by 6 to get 7.5, or the cost of 6 batteries.
Hope this helps!
find the distance between the points E(3,7) and f (6,5)
Answer:
(2,2)
Step-by-step explanation:
If you graph the points out and count from up or down to left or right, I beleive this is the answer you'll get.
Answer:
3.6056 or square root of 13
Step-by-step explanation:
You move right 2 units and left 10 units. You end at (-5, -1). Where did you start?
Answer:
(-13,-1)
Step-by-step explanation:
Moving right means moving positively on the x-axis
Moving left means moving negatively on the x-axis
Follow the equation backwards using the x-coordinate:
Move left 10 units-- -5-10 = -15
Move right 2 units-- -15+2 = -13
Since the y-coordinate did not change, the point you started at is (-13,-1)
Find the value of an that makes each number sentence true 2/3 x N = 1
Answer:
1 1/2
Step-by-step explanation:
n= 3/2
Decimal Form:
n= 1.5
Mixed Number Form:
n = 1 1/2
Are f and g inverses of each other?
Answer:
The answer is: g ( x) and f ( x) are not inverses of each other.
Step-by-step explanation:
This is why you need to check both ways: sometimes there are fussy technical considerations, usually involving square roots, that force the composition not to work, because the domains and ranges of the two functions aren't compatible.
Hope this helps : )