I need help with this problem
Solve the following system of equations using elimination by multiplication.
If the given equations are indeed
[tex]\begin{cases}x-\frac4{5y} = 9\frac45 \\ -14x - 4y = -46\end{cases}[/tex]
we can solve by substitution. Solve the second equation for x :
[tex]-14x - 4y = -46[/tex]
[tex]\implies 7x + 2y = 23[/tex]
[tex]\implies7x = 23 - 2y[/tex]
[tex]\implies x = (23 - 2y)/7[/tex]
Substitute this into the first equation and solve for y :
[tex]\dfrac{23-2y}7 - \dfrac4{5y} = 9\dfrac45[/tex]
On the right side, write the mixed number as an improper fraction:
[tex]9 + \dfrac45 = \dfrac{45}5 + \dfrac45 = \dfrac{45+4}5 = \dfrac{49}5[/tex]
[tex]\implies \dfrac{23-2y}7 - \dfrac4{5y} = \dfrac{49}5[/tex]
Multiply both sides of this equation by 35y (the LCM of the denominator of all three fractions)
[tex]35y \times \dfrac{23-2y}7 - 35y \times \dfrac4{5y} = 35y \times \dfrac{49}5[/tex]
[tex]5y\times(23-2y) - 7\times4 = 7y \times 49[/tex]
[tex]115y - 10y^2 - 28 = 343y[/tex]
[tex]10y^2 + 228y + 28 = 0[/tex]
[tex]5y^2 + 114y + 14 = 0[/tex]
To solve the quadratic, I'll complete the square :
[tex]5\left(y^2 + \dfrac{114}5y\right) + 14 = 0[/tex]
[tex]5\left(\left(y + \dfrac{57}5\right)^2 - \left(\dfrac{57}5\right)^2 \right) + 14 = 0[/tex]
[tex]5\left(y + \dfrac{57}5\right)^2 - \dfrac{57^2}5 + 14 = 0[/tex]
[tex]5\left(y + \dfrac{57}5\right)^2 = -\dfrac{3179}5[/tex]
This system has no real solutions since the square of any real number must be positive.
If we allow complex numbers, we can continue solving to end up with two complex solutions for y,
[tex]\left(y + \dfrac{57}5\right)^2 = -\dfrac{3179}{25}[/tex]
[tex]y + \dfrac{57}5 = \pm i \sqrt{\dfrac{3179}{25}}[/tex]
[tex]y = -\dfrac{57}5 \pm i\dfrac{17\sqrt{11}}5[/tex]
and we can go on to solve for x.
Hence my comment; I suspect you meant to write the system
[tex]\begin{cases}x-\frac45 y = 9\frac45 \\ -14x - 4y = -46\end{cases}[/tex]
because its solution is far simpler. Multiplying through the first equation by 5 gives
[tex]5\times x - 5 \times \dfrac45 y = 5 \times 9\dfrac45[/tex]
[tex]\implies 5x - 4y = 49[/tex]
(since we know 9 + 4/5 = 49/5)
Meanwhile, multiplying through the second equation by -1 gives
[tex]-1 \times (-14x) + (-1) \times (-4y) = -1 \times (-46)[/tex]
[tex]\implies 14x + 4y = 46[/tex]
So if we combine the two equations, we can eliminate y and solve for x :
[tex](5x - 4y) + (14x + 4y) = 49 + 46[/tex]
[tex]\implies 19x = 95[/tex]
[tex]\implies \boxed{x = 5}[/tex]
and solving for y gives
[tex]14x + 4y = 46[/tex]
[tex]\implies 70 + 4y = 46[/tex]
[tex]\implies 4y = -24[/tex]
[tex]\implies \boxed{y = -6}[/tex]
The equation 5y = 6 represents purchasing tubs of yogurt for $6. Which of these equations are equivalent to the equation 5y=6?
a 5y + 4 = 10
b 5y - 1 = 3
c 15y = 18
d 5y = 12
Answer:
blah blah
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
What is the value of the expression?
(514−212)+(623−312)
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
[tex] = { \rm{(514 - 212) + (623 - 312)}} \\ \\ = { \rm{(302) + (311)}} \\ \\ ={ \underline{ \: \: {}^{ - } 9 \: \: }}[/tex]
Suppose line g is the line with equation y=x. Given A(6,-2), B(6,3), and C(-2,-6), what are the coordinates of the vertices of A'B'C' for the reflection?
NEED ANSWER ASAP
Rg
Answer:
A'(-2, 6)B'(3, 6)C'(-6, -2)Step-by-step explanation:
Reflection across the line y=x swaps the x and y coordinates:
(x, y) ⇒ (y, x)
The image points are ...
A(6, -2) ⇒ A'(-2, 6)
B( 6, 3) ⇒ B'(3, 6)
C(-2, -6) ⇒ C'(-6, -2)
If 4 bushels of oats weigh 112 kg, how much do 8. 5 bushels of oats weigh?.
Answer:
238 kg
Step-by-step explanation:
If 4 bushels weight 112, then divide 112 by 4 and you get that each bushel weighs 28 kg. Now multiply that by 8.5.
You need $145 in cash if you withdraw money from your savings account using the ATM how much will you need to withdraw in order to have at least one $145 based upon how ATM’s dispense money?
Answer:
290
Step-by-step explanation:
145 withdrawal free + 145 in cash = 290.
please help will give brainliest
Answer:
Look at the pictures (they are color coded)
red is 1st
blue is 2nd
green is 3rd
black is 4th
Electroboy has been charged up to +96 C which of course causes an electric field to emanate around him. An electroball charged to 2,8 C is thrown at him and gets close enough to experience an electric field of 20 N/C. What is the electric force on the electroball from electroboy's electric field at this moment?
Answer:
static electricty
Step-by-step explanation:
it is preserved charge
Answer:
its electroboom not boy
Step-by-step explanation:
lol its static
Simplify the expression: 4s+10–2+4s
Answer:
8s+8
Step-by-step explanation:
Put it into groups: (4s+4s)+(10-2)=8s+8
Brainliest is appreciated
Answer:
(4s+4s)+(10-2)= 8s/8 =1 so s=1
Step-by-step explanation:
Please help it’s due in an hr
Which of these functions has a y-intercept that is
greater than that of the linear function
represented by the table of values below, and
why?
х
у
2
19
4
13
17
6
7
19
9
23
A. y = x + 9, because the y-intercept of the function
represented by the table of values is 2
B. y=x+9, because the y-intercept of the function
represented by the table of values is 5
C. y = 8x+1, because the y-intercept of the
function represented by the table of values is 2
D. y = 8x + 1, because the y-intercept of the
function represented by the table of values is 5
y = x+9 because the y-intercept of the function represented by the table is 5.
============================================================
Explanation:
Let's focus on the first two rows of the table. Plug those coordinates into the slope formula below.
m = (y2-y1)/(x2-x1)
m = (13-9)/(4-2)
m = 4/2
m = 2
The slope is 2.
Then we'll use something like (x,y) = (2,9) along with the slope we found to determine the y intercept b
y = mx+b
y = 2x+b
9 = 2*2+b
9 = 4+b
9-4 = b
5 = b
b = 5
The equation for the table is y = 2x+5
We can check this by seeing that x = 6 leads to y = 2*x+5 = 2*6+5 = 17. I'll let you check the other x values of the table.
Because y = 2x+5 has a y intercept of 5, we're going to aim for answer choice B. The y intercept of y = x+9 is 9 which is larger than what we just found.
Solve the literal equation for Y:
4=5x+6y
Answer:
y=2/3-5x/6
Step-by-step explanation:
Write an inequality that has the points (-2, -6) and (4, -3) on the line and (6, -4) and (2, -4) as solutions.
(use <= or >= for ≤ or ≥
symbols and write your inequality in y=mx+b form with no spaces)
inequality=
Answer in fraction form is: y ≤ (1/2)x - 5 or [tex]y \le \frac{1}{2}x-5[/tex]
Answer in decimal form is: y ≤ 0.5x - 5
You only need to pick one answer format.
========================================================
Explanation:
The drawing is below.
Let's label the four given points as A,B,C,D
A = (-2,-6)B = (4,-3)C = (6,-4)D = (2,-4)For now, let's focus on the boundary points A(-2, -6) and B(4, -3). A straight line in the form y = mx+b passes through these points. Compute the slope.
m = (y2-y1)/(x2-x1)
m = (-3 - (-6))/(4 - (-2))
m = (-3 + 6)/(4 + 2)
m = 3/6
m = 1/2
m = 0.5
Now let's use one of those (x,y) points along with that m value to find the y intercept b. I'll use the coordinates from point A.
y = mx+b
-6 = 0.5*(-2)+b
-6 = -1 + b
-6+1 = b
-5 = b
b = -5
The equation of the boundary line is y = 0.5x-5 which is the same as saying y = (1/2)x - 5 or [tex]y = \frac{1}{2}x-5[/tex]. We can refer to this as line AB.
-------------------------------
If you were to plot all four points (A,B,C,D) on the same xy grid, then you'd find that point D is on line AB. We're told that point D is a solution to the inequality, which must mean we are going to involve "or equal to" as part of the inequality sign. This will allow points on the boundary to be part of the solution set.
Notice how point C is below line AB. Since point C is also a solution, this means we go for "less than" to shade below the boundary. Overall, the sign we go for is "less than or equal to" or in short ≤
Therefore, the inequality is y ≤ 0.5x - 5
which is the same as writing y ≤ (1/2)x - 5 or [tex]y \le \frac{1}{2}x-5[/tex]
What is the number in standard form (8 x 10) + (2 x 1 /100) + ( 9 x 1/1,000
Answer:
8.0029 x[tex]10^{1}[/tex]
Step-by-step explanation:
8 x 10=80
2 x [tex]\frac{1}{100}[/tex]=0.02
9x[tex]\frac{1}{1,000}[/tex]= 0.009
add all ur answers together and u get 80.029
then in standard form that nwould be 8.0029 x[tex]10^{1}[/tex]
Hoped that helped:P
The probability of event A is 0.53 and the probability of event B is 0.17. The probability of A and B occurring is 0.901. Which statement accurately describes these two events?
Explanation:
We're given that
P(A) = 0.53P(B) = 0.17P(A and B) = 0.901Note that P(A)*P(B) = 0.53*0.17 = 0.0901 which is somewhat similar to 0.901 but not entirely the same. We have an extra zero between the decimal point and the nine. So this indicates that [tex]P(A)*P(B) \ne P(\text{A and B})[/tex]. Therefore, events A and B are not independent. We consider them dependent.
helpp my grades are almost dueeeeeeee,,, but anyway hows yall dayyy?
Answer: c) -1/6, check picture below
Step-by-step explanation:
A computer processes information in nanoseconds. A nanosecond is one-billionth of a second. Write this number as a decimal.
Answer:
0.000000001
Step-by-step explanation:
Let's convert this :
0.000000001
tHT M B
t=tenths
H=Hundredths
T=Thousandths
M=millionths
B=Billionths
what is the answer to 4 3/4 minus 1/3?? Plzz Respond by Tmrw ill give 45 points and brainliest
Answer:
53/12
Step-by-step explanation:
Conversion a mixed number 4 3/
4
to a improper fraction: 4 3/4 = 4 3/
4
= 4 · 4 + 3/4
= 16 + 3/
= 19/
4
To find a new numerator:
a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/
4
= 16/4
b) Add the answer from previous step 16 to the numerator 3. New numerator is 16 + 3 = 19
c) Write a previous answer (new numerator 19) over the denominator 4.
Four and three quarters is nineteen quarters
Subtract: 19/
4
- 1/
3
= 19 · 3/
4 · 3
- 1 · 4/
3 · 4
= 57/12
- 4/12
= 57 - 4/12
= 53/12
pls help. i don't like math
Answer:
X = 5 3/8 (5 and 3 eighths)
Step-by-step explanation:
4/5x = 5 1/5 - 9/10
4/5x = 43/10
x=43/8
x= 5 3/8
Answer:
Exact Form: x=43/8
Decimal Form: 5.375
Mixed number form: x= 5 and 3/8
Step-by-step explanation: here is the steps
Can somebody help me :
Answer:
A
Step-by-step explanation:
Negative numbers are smaller than positive numbers.
Answer:
Your correct 6.55 is a positive number while -6.5 is negitive and positive numbers are always larger then negitive ones
Hope This Helps!!!
Answer this correct and I will give you extra points.
Answer:
he didnt subtract each equations on both sides
5y-6=4y+1
-4 -4
y -6=1
+6=+6
y=7
Step-by-step explanation:
hope that wrk
Marcus has twice as many pens as Bryan. Together they have 36 pens. How many pens does each boy have?
Answer:
Marcus has 24 pens while Bryan has 12 pens.
Step-by-step explanation:
Let u rep 1 unit.
Marcus = 2u
Bryan = u
2u+u=36
3u=36
u=36÷3
=12
No. of pens Marcus has
= 2u
= 2×12
= 24
No. of pens Bryan has
= u
= 12
Plzzz help me it’s due tonight!!!!!
Answer:
UV=5, VW=5[tex]\sqrt{3}[/tex], and m∠U=60
Step-by-step explanation:
sin 30=UV/10=>0.5=UV/10=>UV=5
VW=√(10²-5²)=√75=5√3
m∠U=180-90-30=60
If b = ⟨6,5⟩, and c = ⟨2,9⟩, find a = 5b − 6c.
Answer:
< 18, - 29 >
Step-by-step explanation:
a = 5b - 6c
= 5 < 6, 5 > - 6 < 2, 9 > { multiply each element by the scalar ]
= < 30, 25 > - < 12, 54 > [ subtract corresponding elements ]
= < 30 - 12, 25 - 54 >
= < 18, - 29 >
Answer:
a=(18,-29)
Step-by-step explanation:
You plug (6,5) in for 5b and you plug (2,9) in for -6c so now you get a=5(6,5)-6(2,9) then you cross multiply the 5 and the -6 therefore you get a=(30,25)+(-12,-54) then you add them together getting the answer a=(18,-29).
evaluate 3d/2a, when d=4 and a = -1
Answer:
ok
Step-by-step explanation:
Given that m||n, determine the relationship between ∠9 and ∠15.
The relationship between ∠9 and ∠15 is (c) alternate exterior angles.
There are several relationships that can be formed by angles within the transversal of parallel lines.
From the attached figure, we can see that angles ∠9 and ∠15 are exterior angles of parallel lines m and n.
Because these lines are parallel, then both angles are alternate exterior angles.
Read more about parallel lines at:
https://brainly.com/question/24607467
please help me with this question.
Answer:
Exact Form: 309/25
Mixed Form: 12 and 9/25
Step-by-step explanation:
HELP!! BRAINLIEST!! +15 POINTS!! REAL ANSWERS ONLY PLEASE
what is 65% more of 140
65% more than 140 is 231
the triangles are similar. what is the value of x? enter your answer in the box.
Answer:
l*b*h is the answer of this question
answer this
1) Singapore is located in the +8 time zone. An aeroplane departs from Singapore at 3.00 p.m. (15:00) on Monday and travels across the IDL to Honolulu located in the
-10 time zone. If it takes 12 hours for the journey, find the local time and date when it arrives in Honolulu.
2)An aeroplane departs from Dawson located in the -8 time zone at 6:00 a.m. on
Monday, flies across the IDL and arrives in Tokyo (Japan) in the +9 time zone.
If the flight arrives in Tokyo at 4.00 p.m. on Tuesday, find the time taken for the
journey
Answer:
Local Time = 9:00
Date = Monday
Step-by-step explanation:
Singapore is located in the +8 time zone. An aeroplane
departs from Singapore at 3.00 p.m. (15:00) on Monday
and travels across the IDL to Honolulu located in the
-10 time zone. If it takes 12 hours for the journey, find
the local time and date when it arrives in Honolulu