Solve the simultaneous equations
4x + 3y = 20
4x + 2y = 14

Answers

Answer 1

Step-by-step explanation:

[tex] \underline{ \underline{ \text{Given}}} : [/tex]

[tex] \tt{4x + 3y = 20........... \text{ equation \: ( \: i \: )}}[/tex][tex] \tt{4x + 2y = 14.......... \text{equation \: (ii)}}[/tex]

[tex] \underline{ \text{USE \: ELIMINATION \: METHOD}} : [/tex]

Subtract equation ( ii ) from equation ( i ) :

Remember that the sign of each term of the second expression changes i.e equation ( i ) now becomes -4x -3y = -20

[tex] \tt{ \cancel{4x }+ 2y = 14}[/tex]

[tex] \tt{ \cancel{ - 4x} - 3y = - 20} [/tex]

__________________

[tex] \tt{ - y = - 6}[/tex]

⟿ [tex] \tt{ \boxed{ \tt{y = 6}}}[/tex]

Again , Substituting the value of y in equation ( ii ) :

⟿ [tex] \tt{4x + 2 \times 6 = 14}[/tex]

⟿ [tex] \tt{4x + 12 = 14}[/tex]

⟿ [tex] \tt{4x = 2}[/tex]

⟿ [tex] \boxed{ \tt{x = \frac{1}{2}}} [/tex]

[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : x = \frac{1}{2 } \: and \: y = 6}}}}[/tex]

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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Related Questions

PLZZ HURRY The students at Southern Junior High School are divided into four homerooms. Benjamin just moved into the school district and will be randomly assigned to one homeroom.

Which methods can be used to simulate this situation? Select three options..
Flip a coin 4 times, once for each homeroom, with heads up representing being assigned to the homeroom represented by that flip.
Draw a marble from a bag containing 5 white marbles, 5 black marbles, 5 red marbles, and 5 green marbles, with each color representing a different homeroom.
Use a random number generator with 1, 2, and 12 representing the first homeroom, 7, 9, and 10 representing the second homeroom, 3, 8, and 11 representing the third homeroom, and 4, 5, and 6 representing the fourth homeroom.
Roll a number cube with 1 representing the first homeroom, 2 representing the second homeroom, 3 representing the third homeroom, and any other outcome representing the fourth homeroom.
Spin a spinner with 8 congruent sections with 2 sections assigned to each homeroom.

Answers

Answer:

BCE

Step-by-step explanation:

Answer: (B, C, E)

Step-by-step explanation:

B) Draw a marble from a bag containing 5 white marbles, 5 black marbles, 5 red marbles, and 5 green marbles, with each color representing a different homeroom.

C) Use a random number generator with 1, 2, and 12 representing the first homeroom, 7, 9, and 10 representing the second homeroom, 3, 8, and 11 representing the third homeroom, and 4, 5, and 6 representing the fourth homeroom.

E) Spin a spinner with 8 congruent sections with 2 sections assigned to each homeroom.

I need help with this problemmm, someone help mee!!.

Answers

Answer:

∠A=30°

Step-by-step explanation:

let's call the angle at the bottom B and the one next to the 130 C

∠A=3x-6

∠C=180-130= 50°

vertical angles are equal∠B =8x+4

∠A+∠C+∠B=180°

find x:

3x-6+50+8x+4= 180°

11x+48=180°

11x= 132

x=12

find ∠A

∠A=3x-6= 3(12)-6 =30°

2 + |x-4| = 5
Please help

Answers

Answer:

X=7

Step-by-step explanation:

2 + |x-4| = 5

2 + x -4 = 5

2 + x = 5 + 4

2 + x = 9

x = 9 - 2

x=7

Answer:

x=7

Step-by-step explanation:

2+ x - 4= 5| -2

x-4 =3 | +4

x=7

Mrs. Maytag is purchasing a dryer that sells for $640. She has a coupon for a 15% discount. The sales tax in her area is 72%
What will be the final cost of the dryer?

Answers

Answer

Help me too

Step-by-step explanation:

can someone help me by looking at the picture above??

1. find the mean amount
charged = $ ?

Answers

Answer:  400.89

=======================================================

Work Shown:

To find the average price, we will add up the 9 values in column 2 to get

120+272+358+328+406+392+530+592+610 = 3,608

Then divide that total by 9 since there are 9 values we added up

We get the average to be (3,608)/9 = 400.888 which is approximate. This rounds to 400.89

Side note: It's a bit strange how your teacher mentions "charge in pounds" but then uses a dollar sign.

Step-by-step explanation:

To find the mean, you add all the numbers together then divide by the number of numbers.

Charge : 120+272+358+328+406+392+530+592+610=3608/9=400.888888 =400.89 dollars

The measures of two complementary angles
are in the ratio 7:3. What is the measure of the
smaller angle? What is the measure of the
larger angle?

Answers

The measures of two completely angles are in the ratio 7:3 what is the measure of the smaller angle what is the measure of the larger angle?

If the measures of two complementary angles are in the ratio 7:3. The measure of the smaller and larger angle will be 27.02 and 62.9 respectively.

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that, The measures of two complementary angles are in the ratio 7:3.

The angle is referred to as be complimentary angle when the total of two angles is 90 degrees. For instance, the angles of 30 degrees and 60 degrees complement one another.

Suppose the smaller angle is x and the larger angle is y,

x+y=90 -------(1)

If the measures of two complementary angles are in the ratio of 7:3.

y:x=7:3

7x=3y

y=7/3x

Substitute the value of y in equation 1 as

x+2.333x=90


3.333x=90

x=90/3.33

x=27.02

The measure of the smaller angle is 27.02. The measure of a larger angle is obtained as,

y=90-x

y=90-27.02

y=62.9

Thus, if the measures of two complementary angles are in the ratio 7:3. The measure of the smaller and larger angle will be 27.02 and 62.9 respectively.

Learn more about the angle here:

brainly.com/question/7116550

#SPJ5

Nitric acid is in liquid form if its temperature is between -44°F and 181°F.
At what temperatures will nitric acid be in liquid form?
Choose ALL the correct answers.
-178°F
0°F
192°F
145°F
-41°F
36°F

Answers

option 2, 4, 5, and 6

Answer: 144,36,0,-41

hope this helps :}

Help please this is my grade we are looking at!

Answers

Answer:

D

Step-by-step explanation:

D is the only correct choice

Answer:

D

Step-by-step explanation:

For these questions, give your answers to 1 decimal place.
a) Change 21 out of 71 to a percentage
b) Change 46 out of 154 to a percentage​

Answers

Answer:

a) 29.6%

b)29.9%

Step-by-step explanation:

Here, we want to change the values to percentage form

a) we have this as;

21/71 * 100% = 29.6%

b) we have thus as;

46/154 * 100% = 29.9%

Hi I need help asap

I don’t understand it can u help me for a and b

Answers

Answer:

Hey If you get the answer can you help me bro

Step-by-step explanation:

I am not understanding that either

QUICKK
Solve systems by substitution Find the solution
SHOW ALL WORK

X = 5
-4x + y = -10

( , )

Answers

This is the answer (5,10)

The measure of an angle is 8 degrees less than three times the measure of another angle. If the two angles are supplementary (two angles whose sum is 180) what is the measure of the larger angle?

Answers

Answer:

The measure of the larger is [tex]133^{\circ}[/tex].

Step-by-step explanation:

Given:

The measure of an angle is [tex]8[/tex] degrees less than three times the measure of another angle.

The two angles are supplementary.

To find: The measure of the larger angle.

Solution:

Let the measure of the smaller angle be [tex]x^{\circ}[/tex].

Then the measure of the larger angle be [tex]3x^{\circ}-8^{\circ}[/tex].

The two angles are supplementary, so their sum is [tex]180^{\circ}[/tex].

So, [tex]x^{\circ}+3x^{\circ}-8^{\circ}=180^{\circ}[/tex]

[tex]\Rightarrow 4x^{\circ}-8^{\circ}=180^{\circ}[/tex]

[tex]\Rightarrow 4x^{\circ}=180^{\circ}+8^{\circ}[/tex]

[tex]\Rightarrow 4x^{\circ}=188^{\circ}[/tex]

[tex]\Rightarrow x^{\circ}=\frac{188^{\circ}}{4}[/tex]

[tex]\Rightarrow x^{\circ}=47^{\circ}[/tex]

So, the measure of the smaller angle is [tex]47^{\circ}[/tex].

And, the measure of the larger angle is [tex]3\times47^{\circ}-8^{\circ}=133^{\circ}[/tex].

Hence, the measure of the larger is [tex]133^{\circ}[/tex].

Find the missing angles .

Answers

Answer:

f=60 , c=30

Step-by-step explanation:

there are 2f and 2c in the graph and f=2c

So

f+f+c+c=180

2c+2c+c+c=180

6c=180

c=180/6

c=30

f=2c

f=2×30

f=60

Express 700 as a product of its prime factors in index form.
Write the prime factors in ascending order.

Answers

Answer:

700 = 2² × 5² × 7

Step-by-step explanation:

We need to find 700 as a product of its prime factors in index form.

Prime factors of 700 =2 x 2 x 5 x 5 x 7

= 2² × 5² × 7

So, 700 is equal to 2² × 5² × 7.

Hence, 700 is expressed as a product of its prime factors in index form.

12 (x + 3) = 4 (2x + 9) +4x
is there a solution?????

Answers

Answer:

there is no solution

Step-by-step explanation:

You would use distributive property first to get

12x+36 = 8x+36 + 4x

by combining like terms, you would get 12x+36 = 12x+36, meaning there is no solution to this equation

Select the line segment Please helppppp !!!!

Answers

Answer:

C.

Step-by-step explanation:

A line is straight, and a segment is a part of a line.

A and D and lines because they have the arrows on the side, meaning they keep going and are not a segment.

B is not a line, it curves.

So that leaves C to be the answer because it is the only straight one with no arrows.

9 of 9
A glass is į full. Then 75cm of orange juice is poured in.
The glass is now å full. What is the total volume of the glass?

Answers

Answer:

180 cm³

Step-by-step explanation:

A glass is 1/3 full. Then 75cm³ of orange juice is poured in. The glass is now 3/4 full. What is the total volume of the glass?

Let

x = total volume of the glass

1/3x + 75 = 3/4x

75 = 3/4x - 1/3x

75 = 9x-4x/12

75 = 5/12x

x = 75 ÷ 5/12

x = 75 × 12/5

= 900/5

= 180 cm³

x = 180 cm³

Please Help
0 is the reference angle. Label the hypotenuse, opposite leg, and adjacent leg

Answers

With respect to where theta.

CW is hypotenuse
WO is opposite leg
CO is adjacent leg

expand the expression ​-2.5(-3 + 4n + 8)

Answers

Answer:

2.5+7.5+-10n+-20

Step-by-step explanation:

Multiply everything on the inside by the number on the outside and put it together with addition signs.

-2.5(-3+4n+8)

-2.5*-3=7.5

-2.5(7.5+4n+8)

-2.5*4= -10

-2.5(7.5+-10n+8)

-2.5*8=-20

-2.5+7.5+-10n+-20

Answer: 7.5 + 200n

Step-by-step explanation:

(-2.5 • -3) + (-2.5 • 4n) + (-2.5 • 8)

7.5 + -10n + -20

7.5 + 200n

What’s 5x + 5 factored?

Answers

Answer:

5(x+1)

Step-by-step explanation:

So factor is to make it simplified like x(y+c) {I made up random variable for an example but almost all factored problems look like this}

So first find the Greatest Common Factor or GCF for short

The GCF between 5x and 5 is 5

So you divide the whole thing by 5

5x+5/5

you’d get x+1

Now for the 5 just put it around X+1 but with parenthesis

5(x+1)

HELPPP PLEASE will mark as brainlist

Answers

Answer:

D.  16

Plzzzzz give me Brainliest!!!!!  

A chef uses 2/3 cup of flour for every 1/8 cup of water in a dough recipe. If the chef follows the recipe proportions which statement is true PLEASE SOMEONE HELP ME OUT

Answers

Answer:

What statements =?

Step-by-step explanation:

On Gabriela's first birthday, he parents gave her a $50 savings account. On every birthday after that
her parents added to the account, increasing the amount they deposited by $25 each year. What is the
total amount Gabriela's parents will have deposited into the account by her 18th birthday?

Answers

Answer:

The answer I got was $500

Answer:

$475

Step-by-step explanation:

$25 times 17 years = $425

$50 on 1st year plus the $425 over 17 years

$475

A farmer is building a new silo. The circular silo is 27 meters tall and has a radius of 14 meters. What is the area of the base of the silo? Round your answer to the nearest tenth. Use 3.14 for pi

Answers

Answer:

615.44m²

Step-by-step explanation:

The base of the silo is a circle

Rea of the base of the silo = πr²

r is the radius of the silo

Given

radius r = 14m

Area of the base of the silo = π(14)²

Area of the base of the silo = 3.14(196)

Area of the base of the silo = 615.44

Hence the area of the base of the silo is 615.44m²

Hello! I need some help. Have a blessed day!

Answers

Answer:

false is the correct answer of it if the answer going wrong sorry

false ! have a blessed day as well.

Concrete is made by mixing screenings cement and sand in the ratio 3:1:15. How much sand would be needed to make 125 tons of concrete?

Answers

Answer:

=    98.7 tons

Step-by-step explanation:

ratio =   3:1:15

amount of sand needed =    (15/19)*125      /  3 + 1 +15  =19

Which expression is equivalent to
(32)?
081
0-12
0 0
1
81
12

Answers

Answer:

c

Step-by-step explanation:

1/81

(1/9)^2

Thanks me later ☺️

A cone has a diameter of 4 inches and a height of 7 inches. Find the volume of the cone in terms of π and
using 3.14 for π.

Answers

Answer:

205.25072

Step-by-step explanation:

use the cone calculator

Need help with Geometry proof--thank u

Answers

Step-by-step explanation:

QR is parallel to TU | Given

S is the midpoint of QT | Given

QS = ST | Definition of midpoint

<QSR = <TSU | definition of vertical angles

<QRS = <STU | Definition of Alternate Interior Angles

QSR = TSU | ASA

Pretty sure that's right :D

Also, wherever it says "=", I mean congruency symbol

how do i do these 2 problems please help

Answers

To plot points, you need to first look at the two axis ( The two lines with arrow heads). After looking you can see that there are numbers on each axis. To actually plot points, you will need to place them in this order (X,Y) these are called coordinates. What you need to do now, is simple. You just need to count! The boxes on the grid help with that. Place your finger right where the x and y axis meet. That point is 0. Trace your finger on the paper and move over the x line. When you see the point you need to figure out, stop when your finger is on the same grid line (your finger is on the lines making boxes vertically), be sure to keep in mind that the point does not have to be directly on the axis line, just make sure it’s on the same line going up. From that point, what you need to do is count backwards to that 0 point mentioned earlier. The number that you get is your first number, the y coordinate is the second point you need. To find that you apply the same formula, just going upwards instead of across. Stop moving your finger when you see a point on the same line. When you see it, count backwards again, and the number you get should be the y coordinate. If you still need additional help I have added a picture below which is close to your example. I hope this helps!
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