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]

12 A train in France can travel at a speed
of 217.4 miles per hour. A train in
China can travel 1.23 times this speed.
How fast can the train in China travel
in miles per hour?


I WILL MARK YOU AS BRAINIEST IF YOU ANSWER THIS QUESTION WITH AN ANSWER AND EXPLANATION + 100 points

6.
Two cars A and B 250 km apart are traveling towards each other on the same road. Car A travels at 55 km/h
while car B travels at 70 km/h.
(a) When will they meet on the road?
(b) Find the distance each car travels before they meet.

34z+6= i dont know how to simplify it

45 + 30 = 100 - w


Answer:



Explanation:

PLEASE NO LINKS AND NO NEGATIVITY

Write the converse of the following statement. Then determine its validity.

a. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
b. If a parallelogram is a rectangle, then the diagonals are congruent. TRUE.
c. If a parallelogram is a rectangle, then the diagonals are congruent. FALSE.
d. If the diagonals of a parallelogram are not congruent, then the parallelogram is not a rectangle. FALSE.
d. If a parallelogram is not a rectangle, then the diagonals are not congruent. TRUE.

Chau needs to buy plastic forks. Brand A has a box of 12 forks for $1.12. Brand B has a box of 25 forks for $2.69. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent.

PLEASE HELP!!!!
ASAP!

What is the value of x in AABC?
A. 26
B. 29
C. 32
D. 36

Hello, thanks for the fast reply! I was trying to make sense of the following equation:

8. If the weights of males are normally distributed with mean = 170 and standard deviation = 20, what weight (to the nearest
pound) would correspond with the 40th percentile?
A) 68
B) 165
C) 175
D) 162
E) none of the above

HELP QUICK WILL GIVE BRAINLIEST

write and solve the equation to find the number:
1: the sum of 4 and three times a number is 19
2: ten less the quotient of a number and 3 is 6

Select all the polygons that have reflection symmetry.

A quadrilateral with two pairs of adjacent congruent sides, forming a kite.

A polygon is shaped like a composite figure made up of a rectangle with a small square on its top side and the same sized square on its right side.

A polygon shaped like a five-pointed star in which the left and right sides of the star are mirror images

A six-sided polygon that generally appears as a diagonally-oriented trapezoid attached to a shorter horizontally-oriented rectangle.
Assessment navigation
(added this for all^ my homies with k12 so its easier to find just ignore it)

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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 8 large boxes and 4 small boxes has a total weight of 177 kilograms. A
delivery of 3 large boxes and 2 small boxes has a total weight of 73 kilograms. How much does each type of box weigh?

1. Weight of each large box ____ kilograms

2. Weight of each small box ____ kilograms

PLEASE NO LINKS AND NO NEGATIVITY

Bonjour à tous, pouvez vous m'aider à trouver la réponse pour cette "question ouverte" svp?


Parmi les rectangles de périmètre 100cm, quelles sont les dimensions du rectangle d'aire maximale?

Merci d'avance, Joudy :))

Solve V = twh for w.

please help i need this rn!! ( please tell me how much boxes I color)

Ragnar's bathroom has 148 tiles in it. He found that his kitchen has 7 times as many tiles as his bathroom.

How many tiles are in Ragnar's kitchen?

The sum of two numbers is 25. One number is twice the seond number plus seven.
What are the two numbers?

(X+2)(x+6)=0
In the problem shown, to conclude that x + 2 = 0 or x + 6 = 0, one must use the:

o zero product property
O division property
O transitive property
O multiplication property​

Select the correct answer.
2
Which equation describes the line graphed above?
A.y = -4x - 5
B. y = 5x - 4
C. y = -1/5x - 4
D. y = -4x - 1

Headlights must be used from:

-Sunset to sunrise.

PLEASE SHOW YOUR WORK !!! I REALLY NEED HELP

Someone helppp pls due in 5 min
I will thank

please keep it simple.

PLS ANSWER AS SOON AS POSSIBLE AND I WILL MARK U AS BRAINLIST

How i can answer this question?

HELP HELP PLEASE!!!
consider the function rule: f(x) = 9x -7
a. find f(4)
b. find f(-2)
c. show or explain how the equation 9x - 7 = 65 can be solved using an "undoing process". Report a solution to the equation.