subtract 2 from both sides
3a - 3y = 15 - 2x
factor out the common term 3
3 (a-y) = 15 - 2x
divide both sides by 3
a - y = 15 - 2x/3
add y to both sides
a = 15-2x/3 + y
then solve put the value for a =
15-2x/3 + y + 7 ÷10
simplify using the common denominator
10(15-2x)+7*3/30
simplify 7 * 3 to 21
10(15-2x)+21/30
expand
150-20x+21/30
simplify 150-20x+21 to -20x + 171
-20x+171/30
Answer: -20x+171/30
[tex]\huge\bf Question:– [/tex]
[tex]\sf \longmapsto \: 3a+2x−3y=15[/tex]
[tex] \bf \huge \: To \: Find:–[/tex]
[tex] \boxed{\bf \: Value\: of \: A}[/tex]
[tex]\huge\bf Solution:–[/tex]
[tex]\sf \longmapsto \: 3a+2x−3y=15[/tex]
[tex]\boxed{ \bf \: Add -2x \: to \: both \: sides}[/tex]
[tex]\sf \longmapsto \: 3a+2x−3y+−2x=15+−2x[/tex]
[tex]\sf \longmapsto \: 3a−3y=−2x+15[/tex]
[tex]\boxed{ \bf \: Add \: 3y \: to \: both \: sides}[/tex]
[tex]\sf \longmapsto \: 3a−3y+3y=−2x+15+3y[/tex]
[tex]\sf \longmapsto \: 3a=−2x+3y+15[/tex]
[tex] \boxed{\bf \: \: Divide \: both \: sides \: by \: 3}[/tex]
[tex]\sf \longmapsto \: \dfrac{3a}{3} = \dfrac{−2x+3y+15}{3} [/tex]
[tex] \boxed{\bf \: Cross \: Multiply}[/tex]
[tex]\boxed{\sf \longmapsto \: a = \dfrac{ - 2}{3} x + y + 5}[/tex]
______________________________________
[tex]\bf \: Put\:The\: Value[/tex]
[tex] \sf \longmapsto \: \dfrac{−2x+3y+15}{3} +7÷10[/tex]
[tex] \boxed{\bf \: Distribute}[/tex]
[tex]\sf \longmapsto \: \dfrac{ - 2}{3} x+y+5+ \dfrac{7}{10} [/tex]
[tex] \boxed{\bf \: Combine \: Like \: terms}[/tex]
[tex]\sf \longmapsto \: \bigg( \dfrac{ - 2}{3} x\bigg) + y +\bigg( 5 + \dfrac{7}{10} \bigg)[/tex]
[tex]\sf \longmapsto \: \dfrac{ - 2}{3} x + y + \dfrac{57}{10} [/tex]
______________________________________
[tex]\boxed{\bf The Answer\: is:–}[/tex]
[tex]\boxed{{\underline{\bf\dfrac{ - 2}{3} x + y + \dfrac{57}{10}} }}[/tex]
Find the volume of a cone with a diameter of 12.9 cm and a height of 16.6 cm.
Answer:
112cm^3
Step-by-step explanation:
Formula for volume of a cone is:
[tex] \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]
r = radius and h = height
To find the radius you divide the diameter by 2:
12.9 ÷ 2 = 6.45
Now substitute values into the formula:
[tex] \frac{1}{3} \times \pi \times {6.45}^{2} \times 16.6[/tex]
Which equals 112cm^3
Solve the following system of equations by elimination
Answer:
y = -6
x = 1
Step-by-step explanation:
-x + 2y = -13
-x - 2y = 11
Sum the equations:
-x -x = -2x
+2y - 2y = 0
-13 + 11 = -2
then
-2x = -2
x = -2/-2
x = 1
from the first eq.
-x + 2y = -13
-1 + 2y = -13
2y = -13 + 1
2y = -12
y = -12/2
y = -6
check:
from the second eq.
-x -2y = 11
-1 -(2*-6) = 11
-1 -(-12) = 11
-1 + 12 = 11
sonya has 12 cup box of ceral she wants to pour the cereal into small 1/4 cup snake how many bags of cereal will she have
a- 48
b-36
c- 24
d- 12/48
e-3
Answer:
a - 48
Step-by-step explanation:
12 cups are divided into 1/4 cup bags.
Converting 12 into a fraction, you get:
12/1 divided by 1/4.
When we divide fractions, we flip the second fraction and change the operation to multiplication.
12/1 * 4/1.
Since 12/1 and 4/1 are now just whole numbers, (12 and 4), we can multiply them together.
12 * 4 = 48.
Using Converting The Percentages First Into Fractions, Determine The Following
a) 10% of 120
b) 25% of 16
c) 30% of 20
d) 40% of 25
e) 75% of 48
f) 60% of 140
g) 90% of 50
h) 12.5 of 32
Answer:
a)12
b)4
c)6
d)10
e)36
f)84
g)45
h)4
Help me with this plzzzzzzzzz
Answer:Hi
Step-by-step explanation:
A rule for creating a pattern is given below.
Rule: Subtract 7 from 2 to get y.
Which ordered pair, (x, y), works for the rule?
Answer:
(any real number, 5)
Step-by-step explanation:
Well given that y=7-2 and that y=5, we do not know the value of x, therefore x could be any real number with y being 5. I'm pretty sure that answered your question. So, a example of an ordered pair that would fit this rule would be say (5,5) or (7,5)
Isaac bought 7 chicken wings for $12.60. How much does each wing cost?
Answer:
Each chicken wing costs $1.80.
Explanation:
To find the cost for each wings, you need to split the money by 7 which is: 12.60/ 7
this gives us:
1.80
{(23,4),(-3,8),(-25,-21),(20,13),(21,-14)} what is the domain and range
Answer:
Step-by-step explanation:
The domain: { - 25, - 3, 20, 21, 23 }
The range: { - 21, - 14, 4, 8, 13 }
The slope of line
g
is −12
-
1
2
.
−12
-
1
2
·
·
=
=
−1
Answer:
g
is −12
-
1
2
.
−12
-
1
2
·
·
=
=
−1
(-1,-3); slope 5
PLEASE HELP
I need help find the value of x
identify a possible explicit rule for the nth term of the sequence 9, 17, 25, 33, 41
Answer:
The explicit formula for the nth term of the sequence is [tex]a_n=9+8(n-1)[/tex]
Step-by-step explanation:
Recall:
The explicit formula for a sequence is [tex]a_n=a_1+(n-1)d[/tex] where [tex]a_n[/tex] is the [tex]n[/tex]th term, [tex]a_1[/tex] is the first term, and [tex]d[/tex] is the common difference
Given:
First term --> [tex]a_1=9[/tex]
Common Difference --> [tex]d=8[/tex]
Substitute:
[tex]a_n=9+(n-1)(8)[/tex]
[tex]a_n=9+8(n-1)[/tex]
20% percent tip on 8 dollar
Answer:
9.60 dollars tip is $1.60
Step-by-step explanation:
Pls help! The question is: You are riding a bike up Elm Trail towards Deer trail. You plan to make a left turn on to Deer trail. What is the angle measure of the turn?
Answer:
110
Step-by-step explanation:
there is a angle of 70 in the other side is there is a total of 180 and subtract 70 you get 110
Answer:
110
Step-by-step explanation:
I REALLY NEED HELP WITH QUESTION!! URGENTLY!! ANYONE WHO'S GOOD AT MATHS
Check the picture below.
there are a few angles shaded, I'll call that angle at O ∡O, and that angle at "x" ∡x and the green angle at A, ∡A, and the angle at B, ∡B, just so you know which angle we're referring to.
well, first off let's notice that B and C are points of tangency, meaning we get right-angles as you see in the picture, if we run an angle bisector from ∡x, towards point O, we get two congruent triangles, lemme shorten that up some, 90 + 90 + ∡O +∡x = 360, which means that ∡O + ∡x = 180, meaning that ∡O = 180 - ∡x, if that's so, the angle at point O across the shade, is 360 - ∡O or 360 - (180 - ∡x).
alrighty, by the inscribed angle theorem, ∡A is half of ∡O.
let's now focus on the triangle AOB, we'll be using half of ∡A and half of ∡O and ∡B on that triangle, let's proceed.
[tex]\measuredangle x + \measuredangle O=180\implies \measuredangle O=180-\measuredangle x \\\\\\ \measuredangle A = \cfrac{\measuredangle O}{2}\implies \measuredangle A = \cfrac{180-\measuredangle x}{2} \\\\\\ \stackrel{\textit{the angle across from }\measuredangle O~is}{360-\measuredangle O}\implies 360-(180 - \measuredangle x)\implies 180+\measuredangle x \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\large the sum of all three angles at }\triangle AOB}{\stackrel{\textit{half of }\measuredangle A}{\cfrac{1}{2}\cdot \cfrac{180-\measuredangle x}{2}}~~ + ~~\stackrel{\textit{half the angle across from }\measuredangle O}{\cfrac{180+\measuredangle x}{2}}~~ +~~\measuredangle B~~ =~~180} \\\\\\ \cfrac{180-\measuredangle x}{4}+\cfrac{180+\measuredangle x}{2}+\measuredangle B = 180[/tex]
now, let's multiply both sides by the LCD of all denominators, hmmmm in this case that'll be 4, so multiplying both sides by the LCD will do away with the denominators, so let's do so.
[tex]4\left( \cfrac{180-\measuredangle x}{4}+\cfrac{180+\measuredangle x}{2}+\measuredangle B \right) = 4(180) \\\\\\ (180-\measuredangle x)+2(180+\measuredangle x)+4\measuredangle B = 720 \\\\\\ (180-\measuredangle x)+(360+2\measuredangle x)+4\measuredangle B = 720\implies 540+\measuredangle x+4\measuredangle B = 720[/tex]
[tex]\measuredangle x+4\measuredangle B = 180\implies 4\measuredangle B = 180-\measuredangle x\implies \measuredangle B = \cfrac{180-\measuredangle x}{4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \measuredangle B = 45 - \cfrac{\measuredangle x}{4}~\hfill[/tex]
个,
4800
3. Alexander is taking 15 credit-hours this semester at college. The
relationship between tuition and credit hours is shown by the graph below.
What is the constant of proportionality?
A. 15
B. 400
C. 800
D. 6000
4400
4000
3600
3200
2800
2400
2000
Tuition
1600
1200
800
400
2
3
S
4
Credit Hours
7
&
9
Answer:
4800
3. Alexander is taking 15 credit-hours this semester at college. The
relationship between tuition and credit hours is shown by the graph below.
What is the constant of proportionality?
A. 15
B. 400
C. 800
D. 6000
4400
4000
3600
3200
2800
2400
2000
Tuition
1600
1200
800
400
2
3
S
4
Credit Hours
7
&
9
Step-by-step explanation:
Which function does f(-1/2) ≠ -1
Answer:
anything but 2
Step-by-step explanation:
f(-1/2)
If you plug in 2, you'd get -1. But if you plug in other values, it won't be equal to -1.
A choir teacher is dividing 48 sopranos and 32 altos into singing groups. He wants each
group to have the same combination of sopranos and altos, with no singers left over. What is
the area
Answer:
32
Step-by-step explanation:
x(48 - 2x) = 32
Hope it helps.
help me plsssssssssssssssssssssssssss
Answer:
This answer would be c
Step-by-step explanation:
OMG HELP RN I GIVE BRAINLIST
Which of the following correctly describes the solutions to the inequality?
A.
There are 5 solutions. The solutions are the numbers between 4 and 8.
B.
There are an infinite number of solutions. The solutions are all numbers less than 3.
C.
There are 6 solutions. The solutions are the numbers between -2 and 3.
D.
There are an infinite number of solutions. The solutions are all numbers greater than 3.
Can someone please explain this problem to me? i would really really REALLY appreciate it omg
Answer:
f(0) = 3
f(-2) = -15
Step-by-step explanation:
You just have to plug in the value in f(b) into the b of the equation.
So for f(0) --> 2(0)^3 - |0-4| + 7
2(0) - |-4| + 7
0 - 4 + 7 = 3
------------
for f(-2)
2(-2)^3 -|-2-4| + 7
2(-8) - 6 + 7
-16 -6 + 7 = -15
PLS HELP ME
what is mZA?
Answer:
35+43 = 78 so then E is 78 for both sides. then do 78+18 which is 96. so A is 96. I think
Can someone help me please
Answer:
Step-by-step explanation:
(h, k) = (4, 8)
(y - k) = a(x - h)²
(y - 8) = a(x - 4)²
y = a(x - 4)² + 8
plug in one of the x intercepts (or any other known point on the curve)
0 = a(2 - 4)² + 8
0 = a(4) + 8
a = -2
y = -2(x - 4)² + 8 fourth option.
Answer:
y= -(x-4)^2+8
Step-by-step explanation:
negative graph since the turning point is +ve 4..thus the equation will be (x-4)^2 the y axis is 8 units up therefore the above equation is the answer
A music streaming service conducted a survey asking subscribers where they most often listen to music. Of the 2,500 responses, 1,468 users stated that they most often listen to music while in vehicles.
Use this information to complete the statement. Round all answers to the nearest hundredth.
The approximate sample proportion is ___, which means that ___% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.
Answer:
0.59 and 41%
Step-by-step explanation:
Plato/Edmentum
The approximate sample proportion is o.59, which means that 41% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.
For this situation, the number of positive responses is 1486 out of a total sample size of 2500.
Substitute these values into the formula for sample proportion, where x is the number of positive responses and n is the sample size.
[tex]\hat p = \frac{x}{n}[/tex]
= [tex]\frac{1468}{2500}[/tex]
= 0.59
So, the approximate sample proportion is 0.59.
Since 0.59 represents the proportion who responded favorably, 1-0.59=0.41, represents the proportion which responded unfavorably.
This value of the same as 41%.
So, 41% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.
Therefore, the approximate sample proportion is o.59, which means that 41% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.
Learn more about the sample proportion here:
https://brainly.com/question/33593792.
#SPJ4
The volume of a rectangular prism can be computed using the formula V = lwh.
What is the width of a prism that has a volume of 1664 cubic cm a length of 16 cm and a height of 8 cm?
11 cm
13 cm
26 cm
768 cm
Answer:
13cm
Step-by-step explanation:
substitute values we have into the formula:
1664 = 16 x w x 8
rearrange:
1664/16×8 = w
which equals 13
Answer:
13
Step-by-step explanation: just took the test :)
The larger I grow, the less you can see!
What am I??
Answer: The darkness is the correct answer
Step-by-step explanation:
As you know that if the darkness becomes bigger you are unable to see it. Hope you like the answer do let me know in the about your thoughts.
Find the whole number equal to the fraction below. Enter your answer in the
space provided
Answer:
7
Step-by-step explanation:
42/6= 7
---
its a sort of memorization thing youll know when you do enough of them.
if not, you can divide by smaller parts.
3*2=6 so you can divide 42 by 2, and then 3 if that is easier
42/2
=21
then divide by 3 =7
Answer: 7
Step-by-step explanation: If you simplified 42/6 you would get 7 and 42/6 is basically 42 ÷ 6 which equals 7.
Directions: Compare the sides and angles by filling in the blank with a < or > symbol.
The correct comparison as shown in the figures are:
QR < QSAB > CDm<FJG > m<HJGm<QSP > m<QSRFrom the given diagram, we are to fill in the blank spaces with a < or > symbol.
21) The measure of the angles is a function of the measure of the sides.
Since the angle facing the side QR is less than that of QS, hence QR < QS
22) Similarly for this figure, the angle facing the side AB is greater than that of CD, hence AB > CD
23) Also, for this figure, the side facing the angle m<FJG is greater than the side facing the angle m<HJG, hence m<FJG > m<HJG
24) Also, for this figure, the side facing the angle m<QSP is greater than the side facing the angle m<QSR, hence m<QSP > m<QSR
Learn more on angles here: https://brainly.com/question/16281260
T is the midpoint of RS, T has coordinates (6, 4), and S has coordinates (3,-2). What are the
coordinates of R?
Answer:
help
Step-by-step explanation:
Plz help me i will give u 50pts^_^ and brainliest<3
Answer:
y/x^2=-2x+3
Step-by-step explanation: