Here is a system of linear equations:
6x+21y=103
-6x+23y=51

Would you rather use subtraction or addition to solve the system? Explain your reasoning.

Answers

Answer 1

Step-by-step explanation:

6x + 21y = 103

-6x + 23y = 51

The signs of the x coefficients are opposite.  So adding the equations will eliminate the x terms.

44y = 154

y = 3.5

Answer 2

Combining the equations will remove the x terms because the x coefficients have inverse signs. The solution to the given system of linear equations is x = 4.92 and y = 3.5.

What is the equation?

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

Here is a system of linear equations:

⇒ 6x + 21y = 103

⇒ -6x + 23y = 51

Inverse signs can be seen in the x coefficients. The x terms will therefore be removed after adding the equations.

⇒ 44y = 154

⇒ y = 3.5

Substitute the value of y = 3.5 in the equation 6x + 21y = 103

⇒ 6x + 21(3.5) = 103

⇒ 6x + 73.50 = 103

⇒ 6x = 103 - 73.50

⇒ 6x = 29.50

⇒ x = 4.92

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Related Questions

ITS BEEN AN HOUR LS ILL GIVE BRAINLITST

Answers

Answer:

38.81%

Step-by-step explanation:

Circle area = п r ²

п = 3.14

r = 4 cm

Circle area = 3.14 * (4cm)²

Circle area = 3.14* 16cm²

Circle area = 50.24cm²

Triangle area = (heigth*width)/2

heigth = 2.5 + 4 = 6.5cm

width = 3 + 3 = 6cm

triangle area = (6.5cm*6cm)/2

triangle area = 39cm²/2

triangle area = 19.5cm²

then:

the probability that a randonly select point whitin the circle falls in the shaded area is:

19.5/50.24 = 0.3881     (aprox)

0.3881*100 = 38.81%

When a snack bar opens, the cash register contains at least 50 dollars in $1 and $5 bills. Which of these inequalities represents this situation, where x is the number of $1 bills and y is the number of $5 bills?

Answers

Answer:x + 5y is greater than or equal too $50

Step-by-step explanation:

If x is equal to the amount of $1 then there is no need for a coefficient. Being that y is represented as $5 there needs to be a coefficient of because it’s five dollars times however many you have. Then it is greater than or equal to $50 because the problem states there is at least $50 in the register.

Triangle Z is a scaled copy of Triangle M.

Select all the sets of values that could be the side lengths of Triangle Z.
a. 8, 11, and 14.
b. 10, 17.5, and 25.
C. 6, 9, and 11.
d. 6, 10.5, and 15.
e. 8, 14, and 20.

Answers

Answer:

D and E are correct

Step-by-step explanation:

Here, we want to select the set of values which could be the values of the sides of triangle z.

What we want here are sets of values which is a direct scale up value of the sets of values of triangle M:

We proceed as follows;

a. 8, 11 and 14.

This cannot be correct

Looking at the values of M, 4,7 and 10; We can see that while 4 and 7 are directly scaled up by factor 2 to give 8 and 14, by correspondence, 10 should be 20 and not 11 as in this case.

B. 10, 7.5 and 25

This cannot be correct too. Looking at the way 4 and 10

are scaled up by a value of 2.5; then the value of 7 should be scaled by 2.5 too, but 2.5 * 7 is not 7.5, so this cannot be correct

C. 6 , 9 and 11

This is not correct. In fact, we cannot identify a pattern between these numbers and their values before scaling up

D 6, 10.5 and 15

This looks correct. We can see that the values of triangle M if multiplied by 1.5 each can give these

4 * 1.5 = 6

7 * 1.5 = 10.5

and 10 * 1.5 = 15

e. 8, 14 and 20

Multiplying the sides of triangle M by 2, we can get these values.

4 * 2 = 8

7 * 2 = 14

and 10 * 2 = 20

The scale up value here is simply 2

Answer:

actually it's B, E, and D. At least that's what I got and it said it was correct.

Step-by-step explanation:

Please help me brainiest is award

Answers

Answer:

-3 >-5

5>-4

Step-by-step explanation:

Negative 3 is closer to zero so that statement is true. Also it's obvious 5 is greater than negative 4

hope this helps. Please mark me brainiest          

-3>-5 is the answer and really a map test

Solve for x.

[tex] - 36 + 7x = 76 - x[/tex]

x = [?]​

Answers

Answer:

Hey there!

-36+7x=76-x

-36+8x=76

112=8x

x=14

Let me know if this helps :)

An art studio holds beginners art classes. Each class costs $24 and there is also a one-time registration fee of $15 . You attended c number of classes and paid a total of $687. Find the number of classes you took.

Answers

if you’re looking for a equation it could be “ 24c + 15 = 687 “

The total number of classes that were taken by you was 28.

What is linear equation in one variable?

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question.

Registration fee for the dance class = $15

Amount of money charges for each dance class = $24

Amount of money paid for c number of classes = $687

⇒ [tex]687 = 24c + 15[/tex]

Solve the above linear equation in one variable for c.

[tex]687 = 24c + 15[/tex]

⇒ [tex]687 - 15 = 24c[/tex]

⇒ [tex]672 = 24c[/tex]

⇒ [tex]c = \frac{672}{24}[/tex]

⇒ [tex]c = 28[/tex]

Hence, the number of classes is 28.

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a −3=( a 1 ) 5 what is the value of a?

Answers

Answer:

A=[tex]\frac{-3}{4}[/tex]

Step-by-step explanation:

a−3=a1(5)

Step 1: Simplify both sides of the equation.

a−3=a1(5)

a+−3=5a

a−3=5a

Step 2: Subtract 5a from both sides.

a−3−5a=5a−5a

−4a−3=0

Step 3: Add 3 to both sides.

−4a−3+3=0+3

−4a=3

Step 4: Divide both sides by -4.

-4a/-4 = 3/-4

Your final answer is a=-3/4

Gertrude has 71.502 ounces of butter. How many ounces of butter does she have, rounded to the nearest hundredth?​

Answers

Answer:

71.500

Step-by-step explanation:

502 is closer to 500 than 600.

Answer:

71.50

Step-by-step explanation:

This is because 2 is not up to 5, so it can't be turned into 1 and be added to 0.

The telephone company offers two billing plans for local calls. Plan 1 charges ​$32 per month for unlimited calls and Plan 2 charges ​$17 per month plus ​$0.03 per call.

Answers

Answer:

The indifference point is 500 calls.

Step-by-step explanation:

Giving the following information:

Plan 1 charges ​$32 per month for unlimited calls and Plan 2 charges ​$17 per month plus ​$0.03 per call.

I assume we have to determine the indifference point between the two plans.

First, we need to structure the cost formulas:

Plan 1= 32

Plan 2= 17 + 0.03*x

x= call

Now, we need to equal both formulas:

32 = 17 + 0.03x

15= 0.03x

500= x

The indifference point is 500 calls.

Plan 1= $32

Plan 2= 17 + 0.03*500= $32

Answer:

Step-by-step explanation:

how many class periods that are 3 fourth of an hour long will fit into a school day 6 and 3 fourth hours long

Answers

there will be 9 class periods in 6.75 hours!

The endpoints of AB are at A(1, -6) and B(7,-3). Find the coordinate of the midpoint M of the
segment.

Answers

Answer:

(4,-9/2)

Step-by-step explanation:

(1+7/2,-6-3/2)

(4,-9/2)

can someone help me answer this please

Answers

Answer:

x^2 -14x+49

Step-by-step explanation:

(x-7) ^2

(x-7)(x-7)

FOIL

first ( x*x) = x^2

outer -7x

inner -7x

last -7*-7 = 49

Add these together

x^2 -7x-7x+49

Combine like terms

x^2 -14x+49


Find the lowest common multiple (LCM) of 30 and 42

Answers

Answer:

2-30,42

3-15,21

5-5,7

7-1,7

-1,1

LCM of 30 and 42 is 210

Answer:

210

Step-by-step explanation:

30*42 by HCF of 30,42

1260 by 6 =210

Rewrite as a
simplified fraction.
_
0.1 = ?

Answers

Answer:

1/10

Step-by-step

5. Tinh Tran is a physical therapist. He earns $49,830 a year and is
single with no dependents. The state income tax rate is 5% of
taxable income. What amount is withheld from his biweekly
pay for state income tax?

Answers

Answer:

2491.50$ oooooooooooooooooooooooo

The amount withheld from his biweekly pay for state income tax is $2491.5.

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

We have been given that the physical therapist earns $49,830 a year and is single with no dependents.

To determine the amount withheld from his biweekly pay for state income tax.

Since the state income tax rate is 5% of taxable income.

So the amount withheld from his biweekly pay for state income tax as:

⇒ 5 % of 49,830

⇒ (5/100)49,830

⇒ (0.05)49,830

⇒ 2491.50

Therefore, the amount withheld from his biweekly pay for state income tax is $2491.5.

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What is 1.4 as a fraction in simplest form explain the steps!

Answers

Answer:

7/5

Step-by-step explanation:

What is 1.4 in fraction form? 7/5 is the fraction form of 1.4. 1.4 as a Fraction in simplest form to convert 1.4 to a fraction and simplify to the lowest form.

------------

14/10 = 1.4

7 is half of 14

5 is half of 10

The simplest form of given number is  [tex]\frac{7}{5} [/tex].

Given number is, 1.4

Converted into fraction,  [tex]=\frac{14}{10} [/tex]

It is observed that, 2 is common in both numerator and denominator.

               [tex]\frac{14}{10} =\frac{2*7}{2*5}=\frac{7}{5} [/tex]

Hence, The simplest form of given number is  [tex]\frac{7}{5} [/tex].

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Find the value of x. [Picture below]

Answers

Answer:

56

Step-by-step explanation:

Answer:

56 degrees.

Step-by-step explanation:

a circle is 360 degrees, so 1/2=180 degrees.

all you have to do is take the other degrees, minus them from 180 and you have your answer

Use order of Operations to simplify the following: 4² - (28÷7) + 111

Answers

Answer:

123

Step-by-step explanation:

If the answer is wrong please let me know so I can fix it!!! Have a Great Day :)

Answer:

123

Step-by-step explanation:

16-4+111

12+111

=123

write a two column-proof

Answers

Answer:

1. number each step

2. start with the given informatiom

3. statements with the same reason can be combined into one step

4. draw a picture and mark it with the given information

5. you must have a reason for every statement

6. the order of the statements in the proof is not always fixed , but make sure the order makes logical sense

Find each rate and unit rate $8.96 for 8 pounds of grapefruit?

Answers

Answer:

the answer should be 0.96

30 – 2а — 4) + За
Which expressions are equivalent?

Answers

Answer:

=2456

Step-by-step explanation:23456

Overnight, the temperature in Mayville was – 4°F. But by the following afternoon, the temperature had risen 11°F. What was the temperature in Mayville that afternoon? To solve the problem, Rose added – 4+11 and came up with an answer of 7°F. Is Rose correct? Why or why not?

Answers

Answer:

She is correct. If you add 11 degrees to -4 degrees, you get 7 degrees.

Step-by-step explanation:

-4 + 11 = 7

If b is the midpoint of line AC, and AC = 8x-20, find BC.​

Answers

The Definition Of a Midpoint says that is B is the

midpoint of segment AC, then segment AB ≅ AC.

Since segment AB ≅ segment BC, we can setup

the equation 2(3x - 1) = 8x - 20 and we can solve from here.

Start by distributing the 3 through the parenthses on the left side.

So we get 6x - 2 = 8x - 20.

Now subtract 8x from both sides to get -2x - 2 = -20.

Now add 2 to both sides and we have -2x = -18.

Finally, dividing both sides by -2, we find that x = 9.

If x = 9, segment BC must be 3(9) - 1 or 27 - 1 which is 26.

The box plot is based on the?
mean
median
mode
range

Answers

PLEASE GIVE BRAINLIST

By reading this ithink the answer is B=median

A boxplot is a standardized way of displaying the dataset based on a five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles. Minimum : the lowest data point excluding any outliers.

hope this helped

4.25 -2.5x = 14.75
I need help

Answers

[tex]\text {Hey! Let's Solve this Equation!}[/tex]

[tex]\text {\underline {The First Step is to do Keep Change Change (KCC)}}[/tex]

[tex]\text {Keep: 4.25}\\\text {Change: - into +}\\\text {Change: 2.5x into -2.5x}[/tex]

[tex]\text {\underline {The Next Step is to Flip the Equation}}[/tex]

[tex]\text {Before: 4.25+-2.5x=14.75}\\\text {After: -2.5x+4.25=14.75}[/tex]

[tex]\text {\underline {The Next Step is to Subtract 4.25}}[/tex]

[tex]\text {-2.5x+4.25-4.25=14.75-4.25=10.5}\\\text {-2.5x=10.5}[/tex]

[tex]\text {\underline {The Final Step is to Divide -2.5}}[/tex]

[tex]\text {-2.5x/-2.5=10.5/-2.5}[/tex]

[tex]\text {Remember that Dividing a Positive to a Negative will Equal a Negative.}[/tex]

[tex]\text {Your Answer Would Be:}[/tex]

[tex]\fbox {x=-4.2}[/tex]

[tex]\text {Best of Luck!}[/tex]

Hey there!☺

[tex]Answer:\boxed{x=-4.2}[/tex]

[tex]Explanation:[/tex]

[tex]4.25-2.5x=14.75[/tex]

Let's start by simplifying both sides in the equation.

[tex]4.25+-2.5x=14.75\\-2.5x+4.25=14.75[/tex]

Now we subtract 4.25 from both sides in the equation.

[tex]-2.5x+4.25-4.25=14.75-4.25\\-2.5x=10.5[/tex]

Now in our third/final step, we will divide both sides by -2.5.

[tex]\frac{-2.5x}{-2.5}= \frac{10.5}{-2.5}[/tex]

Now we simplify 10.5/-2.5.

[tex]\frac{10.5}{-2.5}=-4.2[/tex]

[tex]x=-4.2[/tex]

Hope this helps!

A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new position?**

Answers

Answer:
The new position of submarine is 550 feet below the sea level.
Given:
A submarine is located at 800 feet below sea level (i.e) if x is considered as the sea level, then it is located at x - 800. The submarine ascends 250 feet, (i.e) its new position is increased by 250 feet from its previous position, then its new position becomes 800 - 250 = 550 feet. Hence the new position of submarine is located at 550 feet below sea level, x.

Answer:

650

Step-by-step explanation:

800-250=650

It's like taking a negative number and adding a positive number to it

If I add 8.0g of sugar to a cup of tea, and have 2 cups of tea in the morning, how much sugar will I have consumed from drinking tea?

Answers

Answer:

1.6g

Step-by-step explanation:

1 cup of tea= 0.8g

2 cups of tea= 0.8g×2= 1.6g

What is the square root of 10p^3

Answers

Answer:

Factor 10 into its prime factors

          10 = 2 • 5  

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

In our case however, all the factors are only raised to the first power and this means that the square root can not be simplified

At the end of this step the partly simplified SQRT looks like this:

        sqrt (10p3)  

STEP

2

:

Simplify the Variable part of the SQRT

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) sqrt(x8)=x4

    (3.2) sqrt(x-6)=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) sqrt(x5)=x2•sqrt(x)

    (4.2) sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

     SQRT(p3) = p • SQRT(p)  

Combine both simplifications

        sqrt (10p3) =

       p • sqrt(10p)  

Simplified Root :

p • sqrt(10p)

Solve the equation, and check your solution.
-3/5n = -9

Answers

Answer:

-15 = n

Step-by-step explanation:

WILL GIVE BRAINLIEST!!!!!!!!! SOLVE FOR X

Answers

Answer:

15 i think good luck

Step-by-step explanation:

Answer:

15°

Step-by-step explanation:

m<B: Supplementary: 180°-110°=70°

Triangles have an inner angle of 180°. Using this, you can then do:

180°-70°-(30°+20°)=60°

3x+x=60°

4x=60°

x=15°

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