4x + y = 14. 5x +2y = 19 solve the simultaneous equation
Answer:
(3, 2 )
Step-by-step explanation:
Given the 2 equations
4x + y = 14 → (1)
5x + 2y = 19 → (2)
Multiplying (1) by - 2 and adding to (2) will eliminate the y- term
- 8x - 2y = - 28 → (3)
Add (2) and (3) term by term to eliminate y
- 3x + 0 = - 9
- 3x = - 9 ( divide both sides by - 3 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (1)
4(3) + y = 14
12 + y = 14 ( subtract 12 from both sides )
y = 2
solution is (3, 2 )
Step-by-step explanation:
[tex] \underline{ \underline{ \text{USING \: ELIMINATION \: METHOD}}}[/tex]
[tex] \underline{ \underline{ \text{ Solution}}} : [/tex]
[tex] \text{4x + y = 14 - - - - - (i)}[/tex][tex] \text{5x + 2y = 19 \: - - - - - (ii)}[/tex]Multiply equation ( i ) by 2 & Subtract from ( ii ). The equation ( i ) now becomes 8x +2y = 28 { 2 ( 4x + y ) = 2 × 14 }. Remember that while subtracting the sign of each term of equation ( i ) changes and now , it becomes -8x-2y = -28.
[tex] \text{5x + 2y = 19}[/tex]
[tex] \text{ - 8x - 2y = - 28}[/tex]
_____________________
[tex] \text{ - 3x = - 9}[/tex]
Solve for x :
⤑ [tex] \tt{x = \frac{ - 9}{ - 3}} [/tex]
⤑ [tex] \tt{x = 3}[/tex]
Now , substitute the value of x in equation ( ii ) :
⟼ [tex] \text{5 × \: 3 + 2y = 19}[/tex]
⟼ [tex] \text{15 + 2y = 19} [/tex]
⟼ [tex] \text{2y = 19 - 15}[/tex]
⟼ [tex] \text{2y = 4}[/tex]
⟼ [tex] \text{y = 2}[/tex]
[tex] \pink{ \boxed{ \boxed{ \tt{⤿ \: Our \: final \: answer : \boxed{ \boxed{ \tt{x = 3 \: and \: y = 4}}}}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day night ! ♡
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Solve the following rational equation plz help!!
Answer:
x = [tex]\frac{9}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4x}{x+1}[/tex] - [tex]\frac{5}{x}[/tex] = [tex]\frac{4}{x^2+x}[/tex] ← factor denominator
[tex]\frac{4x}{x+1}[/tex] - [tex]\frac{5}{x}[/tex] = [tex]\frac{4}{x(x+1)}[/tex]
[ x ≠ 0, x ≠ - 1 as these would make the terms undefined ]
Multiply through by x(x + 1)
4x² - 5(x + 1) = 4
4x² - 5x - 4 = 4 ( subtract 4 from both sides )
4x² - 5x - 9 = 0 ← in standard form
(x + 1)(4x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
4x - 9 = 0 ⇒ 4x = 9 ⇒ x = [tex]\frac{9}{4}[/tex]
However, x ≠ - 1 for reason given above, then
solution is x = [tex]\frac{9}{4}[/tex]
what is ³/8 of 1 dollar
Answer:
Step-by-step explanation:
A dollar is 100 cents
3/8 = .375
0.375 * 100 = 37.5
Rounded it is 38 cents.
Tasha went golfing. Tasha hit the ball 220 yards down the fairway and then 165 yards to the hole. What would have been the shortest distance had she just hit the ball from the tee area to the hole?
Answer:
385 yards
Step-by-step explanation:
From the information provided we can only assume that the two hits that Tasha performed were in a straight line and in the same direction. Otherwise we would need to know the direction and/or angle of the shots. Assuming they were straight, the shortest minimum distance between the tee area and the hole would be calculated by adding the distance of the two shots.
220 yards + 165 yards = 385 yards
HELP ME PLeaseee!!!!
Answer:
x= 8.5, 2x=17, (9x+5)=81.5
Step-by-step explanation:
since the sum of the interior angles of a triangle is 180 degrees, you must add all of the angles and set them equal 180:
[tex]2x + 2(9x+5) = 180[/tex]
next distribute the 2 to 9x + 5.
[tex]2x + 18x + 10 = 180[/tex]
next combine like terms (2x and 18x) and subtract 10 from 180.
[tex]20x = 170[/tex]
finally, divide 170 by twenty.
[tex]\frac{20x = 170}{20}\\,x=8.5[/tex]
the final answer is x=8.5
once x is determined, you can solve 2x and 9x+5.
[tex]2(8.5)=17\\\\9(8.5) +5 =81.5[/tex]
Hey guys please help!!
Answer:
Yes
Step-by-step explanation:
g(x) = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{1}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{1}{4}[/tex] ....... (1)
(1) × 4
4y = - x + 1
x = - 4y + 1
y = - 4x + 1
f(x) = - 4x + 1
∴ f(x) and g(x) are inverses
Kara ran 5 miles yesterday. She ran again today. Her total distance for
both days is 6.5 miles. If she ran at a pace of 6 miles per hour today,
how long did Kara run today?
9514 1404 393
Answer:
15 minutes
Step-by-step explanation:
We can let t represent the time in hours that Kara ran today. Then her distance today is ...
distance = speed · time
distance = 6t
Her total distance for both days is ...
5 + 6t = 6.5
6t = 1.5 . . . . . . . . . . subtract 5
t = 1.5/6 = 1/4 . . . . . divide by 6
Kara ran 1/4 hour today. That is 15 minutes.
Two equations that would have a solution of (3,6)
Answer:
[tex]1) y=2x\\2) y=x+3[/tex]
Step-by-step explanation:
[tex]1) y=2x\\2) y=x+3[/tex]
Hope I helped!
Check out my profile for more answers!
what is the slope of (4,6) and (-6,2)
Answer:
2/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-6)/(-6-4)
m=-4/-10
simplify
m=2/5
Answer:
Step-by-step explanation:
Slope is m=(y2-y1)/(x2-x1)
m=(2-6)/(-6-4)
m=-4/-10
m=2/5
What is the measure of angle ABD in trapezoid ABCD?
24°
40°
64°
92°
The sun of two numbers is 36. The larger number is 18 more than the smaller number. What are the numbers?
Answer:
Step-by-step explanation:
a+b=36
lets name the 2 numbers a,b
b=a+18
a+a+18=36
2a=36-18
2a=18
a=9
b=27
Answer:
the numbers are 9 and 27
Step-by-step explanation:
equation to the problem: x+y=36
one number (y) is 18 times greater than the other number (x): x+18=y
plug in the 2nd equation to the first equation (systems of equations):
x+(x+18)=36
solve the equation:
2x+18=36
*minus 18 on both sides*
2x=18
*divide the whole equation by 2 to get the value of just one x*
x=9
since variable x is the n smaller number, add 18 to 9 to get the 2nd number:
18+9= 27
y=27
Select the correct answer.
What is the value of y in the triangle?
y
30°
60°
6
O A.
3
OB. 6
C. 673
D.
33
This is a special kind of right triangle, called a 30-60-90 triangle.
Across from the 30 degree angle, the side is equal to x. Across from the 60 degree angle, the side is equal to x[tex]\sqrt{3}[/tex]. And across from the 90 degree angle, the side is equal to 2x.
Using what we know about 30-60-90 triangles, lets first solve for x. We know that the hypotenuse, given, is equal to 6.
2x = 6
x = 3
Then, we are looking for the side opposite of the 60 degree angle. So its value is x[tex]\sqrt{3}[/tex].
x = 3
3 * [tex]\sqrt{3}[/tex] = 3 [tex]\sqrt{3}[/tex]
y = 3[tex]\sqrt{3}[/tex] (option D)
Hope this helps!! :)
The value of y for the given triangle will be 3√3, hence option (D) will be correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
Right angle triangles are triangles in which one angle is 90°.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
Given a right-angle triangle
Let the side opposite to 30° is perpendicular and the remaining y will be base.
By trigonometric relation
cosx = base/hypotenuse
cos30° = y/6
y = 6 × cos30° ⇒ y = 6 × √3/2
y = 3√3 hence the value of the hypotenuse or y will be 3√3.
For more about triangles,
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Help Please! I'll give branliest!
Two airplanes leave the airport. Plane A departs at a 42° angle from the runway, and plane B departs at a 44° angle from the runway. Which plane was farther away from the airport when it was 7 miles from the ground? Round the solutions to the nearest hundredth.
Plane A because it was 9.428 miles away
Plane A because it was 10.46 miles away
Plane B because it was 10.08 miles away
Plane B because it was 9.73 miles away
Answer: plane a because it was 10.46 miles away
Step-by-step explanation:
Pls help I hate math
A water container in the shape of a rectangular prism has a length of 2 meters, a width of 3/4 meter, and a height of 1/2 meter. If a cubic meter of water costs $1.20, what is the cost to fill the container?
Answer:
look below!
Step-by-step explanation:
For the length I think you meant 32, and if you did it is $14.40
If not and you meant length of 2 it is $0.90
Answer:
lxwxh for volume.
2x.75x.5 = .75 cubic meters.
.75 percent of 1.20 = .90.
90 cents is the answer.
Cheyenne bought 60 tickets for rides at an amusement park. Each ride costs 4 tickets, and Cheyenne has been on x rides so far. Write an expression is equivalent to the number of tickets that Cheyenne has left?
Answer:
x=number of rides taken
y=number of tickets left
60=4(x)+y
c) El 9 % de 700 =
d) El 15 % de 6 000 =
Help please ill give 20 points
Answer:
15
Step-by-step explanation:
Answer:
4r^12 t^2
Step-by-step explanation:
Use the exponants : ( 8r^6t^3 )/4t^2
simplifie :( 2r^6t^3 )/t^2
Use the exponent : ( 2r^6t^3 )/t^2 = 4r^12t^2
14 pencils cost £3.36. How much would 8 pencils cost?
Answer:
£1.92
Step-by-step explanation:
3.36/14 will give you the cost of each pencil
£0.24 is the cost of one pencil
8 pencils will cost you £1.92
Simplify the expression [tex]5^{3}[/tex] × [tex]5^{-5}[/tex]
A. 1/5
B. 1/5^2
C. -5^2
D. 5^2
Which of the following situations could be modeled with a parabola that is concave up? a rocket that is launched into the air a rope bridge a soccer ball being kicked across the field the flow of the water from a water fountain
Answer:
djdjfjfjfhfhfhd ch fmdknfrus M dnqjw
In a fruit survey , 30 children choose their favourite
fruit out of apples, bananas and watermelon.10% choose
apples, 30% choose bananas. How many children choose
watermelon?
Answer:
60%
Step-by-step explanation:
How much more would Keri's monthly loan payment be if she got a 5% loan for 5 years?
$
more per month
$9436 EMI Keri has to pay for $500,000 loan at the rate of 5% for 5 years.
What is EMI?equated monthly instalment or EMI relates to payments made regularly to repay an outstanding loan within a certain time frame.
Given loan rate is 5% and time period is 5 years let total amount is $500,000. Formula for EMI Calculation is -
P x R x (1+R)^N / [(1+R)^N-1] where-
P = Principal loan amount.
N = Loan tenure in months.
R = Monthly interest rate.
R = Annual Rate of interest/12/100.
Putting these values in above equation
EMI = 500000 *5* *(1 + 5%)^60 / [(1 + 5%)^60]
EMI = 9436
Therefore, Keri must pay a $9436 EMI on her $500,000 loan over five years at a rate of 5%
Learn more about EMI here:
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Find the slope of the line
y=-6/5x + 4/9
Answer:
-6/5
Step-by-step explanation:
slope =coefficient of x
Lily begins solving the equation 4(x-1)-x=3(x+5)-11. Her work is shown below. 4(x-1) - x = 3 (x+5)-11 4x −4) −x =3x +15 −11 3x-4= 3x+4 How can her solution be interpreted? The equation has no solution The equation has one solution: x=0x=0. The equation has infinitely many solutions. The equation has one solution: x=8x=8.
Answer:
Um...
Step-by-step explanation:
Hai
Factor each expression by finding the GCF.
8 + 16 =
8 ( 1 + 16)
2 (4 + 16)
8 ( 1 + 2)
4 (2 + 6)
Select all possible solutions for 2x + 7 < 3x - 5.
Answer:
7<x-5
12<x
x>12
Step-by-step explanation:
1/4 : 10 = x : 4 solve for x
Answer:
Step-by-step explanation:
1/4 :10=1/40
1/40=x/4
x=4/40=1/10
equivalent Find the number that makes the ratio equivalent to 1:7. 4:
Answer:
28
Step-by-step explanation:
Ratios are like fractions. Since you're finding an equivalent ratio, u can set them up like equivalent fractions and put an x where the missing number would go:
[tex]\frac{1}{7} = \frac{4}{x}[/tex]
You can either cross multiply and then solve for x, but it's easier to just think about it. The fractions are equivalent, right? So for them to be the same you'd have to do to the bottom what u do to the top.
To get from 1 to 4, you multiply by 4. By that logic, to get from 7 to x you'd have to multiply by 4 as well. Therefore x = 7x4, which is 28.
So x = 28
*** PLEASE HELP*** 1. What does 4x + 10x = and 2.Which expression is an example of having like-terms?
4x + 4y
4x2 + 5y2
5x + 3x
8 - 4x
Answer:
1. 14x
2. 5x + 3x
Step-by-step explanation:
1) 4x + 10x = 14x
2) By "like-terms" the question means that the expression contains the same variable part. Therefore, the only expression that meets that is 5x + 3x.
1
What is the slope of this non-vertical line? Use your transparency if needed.
3
There’s no further instructions on this please help
Please help
Answer:
Assuming that the line is completely horizontal, that the 1 at the top is indicating the question number, and that the 3 is the only other piece of information given about the line, I think it's y = 3. I hope this is right, sorry because that's a terrible question. Good luck!