3x - 5y = 4, -2x + 6y = 18 (system of equations)

[tex]\longmapsto[/tex]The value of "x" is 5.

[tex]\large\underline{\sf{Solution-}}[/tex]

Given that,

A trapezium ABCD in which AB || CD such that

Now,

[tex]\rm In \: \triangle \: AOB \: and \: \triangle \: COD[/tex]

[tex]\rm \: \angle \: AOB \: and \: \angle \: COD \: \: \{vertically \: opposite \: angles \}[/tex]

[tex]\rm \: \angle \:ABO \: and \: \angle \: CDO \: \: \{alternate \: interior \: angles \}[/tex]

[tex]\bf \: \triangle \: AOB \: \sim \: \triangle \: COD \: \: \: \{AA \: similarity \}[/tex]

[tex]\bf\longmapsto\:\dfrac{AO}{CO} = \dfrac{BO}{DO} [/tex]

[tex]\rm \longmapsto\:\dfrac{x - 1}{x + 1} = \dfrac{x + 1}{x + 4} [/tex]

[tex]\rm \longmapsto\:(x - 1)(x + 4) = {(x + 1)}^{2} [/tex]

[tex]\rm \longmapsto\: {x}^{2} - x + 4x - 4 = {x}^{2} + 1 + 2x[/tex]

[tex]\rm \longmapsto\: 3x - 4 = 1 + 2x[/tex]

[tex]\rm \longmapsto\: 3x - 2x= 1 +4[/tex]

[tex]\bf\longmapsto \:x = 5[/tex]

You are running a fuel economy study. One of the cars you find is blue. It can travel 30 and one half miles30 1 2 miles on 1 and one fourth gallons1 1 4 gallons of gasoline. Another car is red. It can travel 25 and three fifths miles25 3 5 miles on four fifths gallon 4 5 gallon of gasoline. What is the unit rate for miles per gallon for each​ car? Which car could travel the greater distance on 1 gallon1 gallon of​ gasoline?

Blue car: 30.5 / 1.25 =24.4 miles per gallon

Red car: 25.6/0.80   =32 miles per gallon

You can easily see that the Red car travel farther on 1 gallon of gasoline.

Answer:

The unit rate for the blue car is 24 2/5 and The unit rate for the red car is 34

Answer:

It's not proportional

Step-by-step explanation:

The first 2 days are proportional because, they travel at an increment of 60 miles an hour.

But, on the third day, it is not proportional because they travel at an increment of 90 miles an hour.

360 / 4 = 90

120 / 2 = 60

60 / 1 = 60

Answer:

The answer would be yes and no!! But, it would be no!

Step-by-step Explanation:

Yes: On Monday and Tuesday, those would be proportional because they are just counting by 60´s. 60 plus 60 would give you 120.

No: On Wednesday, this ¨person¨ traveled 360 miles in 3 hours. Now, you aren´t counting by 60´s anymore. Even though you started out counting by the 60´s, doesn´t mean you will finish like that.

60´s:

1 hour = 60 mi

2 hours = 120 mi

3 hours should be = 180 miles, not 360 Because:

360 mi would be equal to 6 hours. Do you see where I´m going with this?

Hope that helps you so you can put it in a mathematical way. Have a great day!!

If you get it wrong, plz notify me any way possible...... :)

Answer:

Not a function

Step-by-step explanation:

The an x-value (the first number in your ordered pair)ca not appear in another ordered pair.  It it does, you do not have a function.

( -7,1)(-5,3)(-7,-1)(5,13)  -7 appears as the first number in two of your ordered pairs.  Not a function!

Answer:

the answer will be something like 18

Answer:

$5.29 per pair of socks

Step-by-step explanation:

26.45/5=5.29

Answer:

x =√969

Step-by-step explanation:

AC²=AB²+BC². (Formula)

(35)²=(16)²+BC²

1225-256=BC²

969=BC²

BC=√969

Answer:

40

Step-by-step explanation:

It is 40 because on the graph it shows that you don't start at the first crate but the 2nd you do and you have to figure out if the crate was one how many apples would their be

[tex]\displaystyle \frac{1}{x} +\frac{1}{3x} =4 \ \ ; \ \ x\neq 0 \\\\\\ \frac{3+1}{3x} =4 \\\\\\12x=4 \\\\ \boxed{x=\frac{1}{3} }[/tex]

I started by labeling the right angle (Angle C) 90º. Next, I wrote down everything in one equation.

2x + 90 + 3x - 20 = 180º (180 degrees in a triangle)

Next, I add 20 on both sides.

2x + 90 + 3x = 200º

I combine like terms (2x and 3x)

5x + 90 = 200º

I subtract 90 from both sides.

5x = 110º

Divide 110 by 5 to get x.

x = 22

======

For problem two, I label all the angles I know.

49º + 80º + r = 180º

I add 80 and 49.

129º + r = 180º

I subtract 180 and 129 and get 51º, which is your angle for R.

For angle X, you know that angle R plus angle X equals half of a circle, which is 180º

We know from before that 129º is 180º without R, so X is 129º

I hope this helps! Let me know if I'm wrong!

Queremos saber cuantas porciones de arroz se preparan dado que conocemos cuantos gramos de arroz se utilizan.

Se prepararon 68 porciones.

Lo que sabemos en principio es que, por cada porción de arroz, se necesitan 70 gramos de arroz.

Sabemos que en total se utilizan 4,760 gramos de arroz. Para saber cuantas porciones se prepararon, hay que tomar el cociente entre la cantidad total utilizada y lo que se usa para cada porción.

Esto nos da:

4,760g/70g = 68

Es decir, se prepararon 68 porciones.

Sí quieres aprender más, puedes leer

https://brainly.com/question/18070326

100-meter rise, 72-meter descent followed by a 48-meter rise

100-72+48 = 76

after these 20 seconds, they are 76 meters higher than at the start of the ride

Answer:

290

Step-by-step explanation:

30x2 + 20x4 + 50x3

Hope this helps. Please mark brainliest if you would. It would really help me out

Answer:

290

Step-by-step explanation:

30x2+4x20+3x50 multiply first and you get 60+80+150=290

Answer:

x = 2.4

Step-by-step explanation:

10x = 24

x = 24 ÷ 10

x = 2.4

Step-by-step explanation:

→ -4 = 20 - 10x

→ -20 - 4 = 10x

→ -24 = 10x

→ x = -24/10

→ x = -2.4

therefore, value of x is -2.4

hope this answer helps you dear!

Answer:

2

Step-by-step explanation:

F(3) means that we plug in 3 for the x value of the original equation, and F(4) means that we plug in 4 for the x value of the original equation

F(3) = -2(3) + 3

= -3

F(4) = -2(4) + 3

= -5

- 3 -(-5) = 2

Answer:

2

Step-by-step explanation:

Step 1: Solve for f(3)

Step 2: Solve for f(4)

Step 3: Subtract f(4) from f(3).

Therefore, the answer is 2.

The property used is Division property of equality to get the resulting equation since we divided both sides by 3

Given the inequality expression

3 (−13 x − 23) ≥ 3(7x + 3)

We are to know which of the property is used to arrive at  − 13 x − 23 ≥ 7x + 3

We can see that both sides of the expression were divided by 3 as shown:

[tex]\frac{3(-13x-23)}{3} \geq \frac{3(7x+3)}{3}\\-13x-23 \geq 7x+3\\[/tex]

From the division, we will see that the property used is Division property of equality to get the resulting equation since we divided both sides by 3

Learn more here: https://brainly.com/question/15816805

Answer:

i have no idea

Step-by-step explanation:

Answer:

They won 10 matches

Step-by-step explanation:

Since it's 2/3 if you multiply 3 by 5 you get 15. If you multiply 2 by 5 you get 10. So wit would be 10/15 which is also 2/3.

Answer:X=5

Step-by-step explanation:took the test

Answer:

Line passing through (2,2) is parallel to X - 2Y = 4, so, the slope is same as given line.

m = -a/b = -1/-2 = 1/2

The equation is

(Y - Y1) = m(X - X1) => Y - 2 = 1/2(X - 2) =>

2Y - 4 = X - 2 => | X - 2Y = -2 |

Inequalities are used to compare unequal expressions.

The actual comparison is:[tex]\mathbf{-3.5 < 5}[/tex] or [tex]\mathbf{5 > -3.5}[/tex]

The temperatures are given as:

[tex]\mathbf{Temperature = -3.5F,\ \ 5F,\ \ 1.5F,\ \ -0.5F,\ \ -2F,\ \ 2.5F,\ \ -4F}[/tex]

From the above list, we have:

[tex]\mathbf{Day \ 1= -3.5F}[/tex]

[tex]\mathbf{Day \ 2= 5F}[/tex]

By comparison,

[tex]\mathbf{-3.5 < 5}[/tex] or [tex]\mathbf{5 > -3.5}[/tex]

Using absolute values, the inequalities are:

[tex]\mathbf{|-3.5| < |5|}[/tex] or [tex]\mathbf{|5| > |-3.5|}[/tex]

Hence, the actual comparison is:

[tex]\mathbf{-3.5 < 5}[/tex] or [tex]\mathbf{5 > -3.5}[/tex]

Read more about inequalities and absolute values at:

https://brainly.com/question/24797699

Answer:

bobo ka ba

Step-by-step explanation:

name!https://youtu.be/vA3qDEMnB5k

Answer:

6/9+6/9

find the LCM, which is 9

9÷9=1, 1×6=6

since it is the same thing

6+6/9 = 12/9

= 1 whole number 3/9 or 1 whole number 1/2

Answer:

slope is -2/3

Step-by-step explanation:

[tex]3y = - 2x + 6 \\ y = \frac{ - 2}{3} x + 2[/tex]

Answer:

Which expression is equivalent to m-2m-6m?

if this is correct can i have brainliest

Answer:$216

Step-by-step explanation:

you do 18 * 12 because he gets 18 every month and there are 12 months in a year

Answer:

27h+16=178 I believe would work as an equation for this problem

Step-by-step explanation:

The required time to plant the rest of the saplings is 6 hours, and 27 + 16 = 178 is the required expression.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the number of hours be h,
He can plant 27 saplings per hour.
He needs to plant 178 total saplings and has already planted 16 saplings.
So, according to the quesiton,
27h + 16 = 178,
27h = 162
h = 162/27

h = 6

Thus, the required time to plant the rest of the saplings is 6 hours,

Learn more about models here:
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#SPJ2

Answer:

10

Step-by-step explanation:

Answer:

I thin the asnweris 60

Step-by-step explanation:

Let me know if i'm right I don't know if I followed all the steps

Answer:

x

=

−

0.3559322

Step-by-step explanation: