Here is a system of linear equations
2x+3y=14
4x-3y=10

Which would be more helpful for solving the system: adding the two equations or subtracting one from the other?

~Shoto Todoroki here~

Y=(x+4)(−x+6)

Hope this helps :D

Answer: B

Step-by-step explanation:

JK = 6.08

JL = 5.83

using distance formula is √[(x2 – x1)^2 + (y2 – y1)^2].

Answer:

the fourth

Step-by-step explanation:

Complementary means that the sum of two angels equals to 90°

so LKM and MKN because they're both 45° and the sum is 90°

Answer:

a

Step-by-step explanation:

Answer:

I believe the answer is 1

Step-by-step explanation:

Hope that helps!

Answer:

10 and 11, The square root of 109 is approximately 10.4 and the two consecutive numbers are 10 and 11.

Answer: 2

Step-by-step explanation:

1/4 ÷ 1/8 = 1/4 x 8 = 8/4 = 2

The extraneous solution is the value of the independent variable for which the problem has no solution. x=3 is an extraneous solution.

An extraneous solution is a solution that develops from the process of addressing the problem but is not a real solution to the problem, such as an equation.

In order to know the extraneous solution, we need to find the value of x in the given equation,

[tex]\rm log_4(x)+log_4(x-3)= log_4(-7x+21)[/tex]

Using the logarithmic property,

[tex]\rm log_4[x(x-3)]= log_4(-7x+21)[/tex]

Taking the anti-log, we will get,

[tex]x(x-3)= -7x+21\\\\x^2-3x=-7x+21\\\\x^2+7x-3x-21=0\\\\x(x+7)-3(x+7)=0\\\\(x-3)(x+7)=0[/tex]

If we substitute the factors with the 0, we will get the value of x as 3 and -7.

We know that extraneous solutions are those solutions, which when substituted in the initial equation, the equation does not return an equation.

x=3

[tex]\rm log_4(x)+log_4(x-3)= log_4(-7x+21)[/tex]

[tex]\rm log_4(x3)+log_4(3-3)= log_4(-21+21)\\\\\rm log_4(x)+log_4(0)= log_4(0)[/tex]

As the value of logₐ(0) is undefined, therefore, x=3 is an extraneous solution.

Learn more about Extraneous solutions:

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Answer:

B. x = -3

Step-by-step explanation:

Answer:

Simplify   —

           3

Equation at the end of step

1

:

                        5    

 (((6 • (x2)) -  7x) -  —) -  x

                        3    

STEP

2

:

Equation at the end of step

2

:

                     5    

 (((2•3x2) -  7x) -  —) -  x

                     3    

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

                6x2 - 7x     (6x2 - 7x) • 3

    6x2 - 7x =  ————————  =  ——————————————

                   1               3      

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  6x2 - 7x  =   x • (6x - 7)

Adding fractions that have a common denominator :

4.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (6x-7) • 3 - (5)     18x2 - 21x - 5

————————————————————  =  ——————————————

         3                     3      

Equation at the end of step

4

:

 (18x2 - 21x - 5)    

 ———————————————— -  x

        3            

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

        x     x • 3

   x =  —  =  —————

        1       3  

Trying to factor by splitting the middle term

5.2     Factoring  18x2 - 21x - 5

The first term is,  18x2  its coefficient is  18 .

The middle term is,  -21x  its coefficient is  -21 .

The last term, "the constant", is  -5

Step-1 : Multiply the coefficient of the first term by the constant   18 • -5 = -90

Step-2 : Find two factors of  -90  whose sum equals the coefficient of the middle term, which is   -21 .

     -90    +    1    =    -89

     -45    +    2    =    -43

     -30    +    3    =    -27

     -18    +    5    =    -13

     -15    +    6    =    -9

     -10    +    9    =    -1

     -9    +    10    =    1

     -6    +    15    =    9

     -5    +    18    =    13

     -3    +    30    =    27

     -2    +    45    =    43

     -1    +    90    =    89

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

5.3       Adding up the two equivalent fractions

(18x2-21x-5) - (x • 3)     18x2 - 24x - 5

——————————————————————  =  ——————————————

          3                      3      

Trying to factor by splitting the middle term

5.4     Factoring  18x2 - 24x - 5

The first term is,  18x2  its coefficient is  18 .

The middle term is,  -24x  its coefficient is  -24 .

The last term, "the constant", is  -5

Step-1 : Multiply the coefficient of the first term by the constant   18 • -5 = -90

Step-2 : Find two factors of  -90  whose sum equals the coefficient of the middle term, which is   -24 .

     -90    +    1    =    -89

     -45    +    2    =    -43

     -30    +    3    =    -27

     -18    +    5    =    -13

     -15    +    6    =    -9

     -10    +    9    =    -1

     -9    +    10    =    1

     -6    +    15    =    9

     -5    +    18    =    13

     -3    +    30    =    27

     -2    +    45    =    43

     -1    +    90    =    89

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 18x2 - 24x - 5

 ——————————————

       3      

Step-by-step explanation:

Using compound interest, it is found that:

a) $1,270.70 will be in the account after 6 years.

b) It will take 17.53 years for the $1000 to double.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

In this problem, the parameters are given as follows:

[tex]A(0) = 1000, r = 0.04, n = 12[/tex]

Item a:

Over 6 years, that is t = 6, thus:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 1000\left(1 + \frac{0.04}{12}\right)^{12 \times 6}[/tex]

[tex]A(t) = 1270.7[/tex]

$1,270.70 will be in the account after 6 years.

Item b:

This is t for which A(t) = 2P = 2000, hence:

[tex]2000 = 1000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]

[tex](1.0033)^{12t} = 2[/tex]

[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]

[tex]12\log{(1.0033)} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]

[tex]t = 17.53[/tex]

It will take 17.53 years for the $1000 to double.

More can be learned about compound interest at https://brainly.com/question/25781328

Answer:

B. [tex]x^2+11x+24\leq 150[/tex]

Step-by-step explanation:

Step 1) Defining Sue and Jeremy's ages using x

Sue is 3 years older than Holly (h):

[tex]h=x+3[/tex]

Jeremy is 5 years older than Sue, or 8 years older than Holly (j):

[tex]j=x+8[/tex]

Product of Jeremy and Sue's ages is less than or equal to 150:

[tex]hj\leq 150[/tex]

Step 2) Simplifying into a single equation

Using the equation above we can substitute Sue and Jeremy's ages:

[tex](x+3)(x+8)\leq 150[/tex]

Now we can simplify this equation. Use the distributive property first:

[tex]x(x+8)=x^2+8x\\3(x+8)=3x+24[/tex]

Now add all the terms together and get the final answer:

[tex]x^2+8x+3x+24\leq 150\\x^2+11x+24\leq 150[/tex]

Final equation: [tex]x^2+11x+24\leq 150[/tex]

Answer:

r = sqrt(16/pi)

Step-by-step explanation:

Cylinder formula = r^2 x pi x height

176 pi/11pi = 16

16 = r^2 x pi

16/ pi = r^2

r = sqrt(16/pi)

Answer:

25.

Step-by-step explanation:

the ratio from even to odd is equal. a half chance of getting even 3:6 & 4:8 [ theres 3 even #s on the cube, 3 odds #s on the cube] vice VERSA!! for either even or odd roll. so out of 50, half of 50 is 25. there's a 1:2 chance of even(or in whatever case) 1:2 = 25:50

Answer:

it will take the second crocodile 60 seconds

The time it will take the second crocodile to finish it's snack is; 120 s

Let x represent the rate of the first crocodile and let y represent the rate of the second crocodile.

The two crocodiles working together can finish a snack in 40 seconds. Thus;

(1/x + 1/y)40 = 1

It takes one of the crocodiles 60 seconds to finish it's snack. Thus;

(1/x + 1/60)40 = 1

40/x + 2/3 = 1

x = 120 seconds

Read more about rate of work at; https://brainly.com/question/12442233

Answer:

so i don't  know  the answanswer

Step-by-step explanation:

i son't  know  go  learn

Answer:

16+3i

Step-by-step explanation:

(9+ 14¡) + (7 - 11¡)

9+ 14¡ + 7 - 11¡

16 + 3i

Answer:

How to succeed in 7th grade

Strive for a deeper understanding of science. Instead of just memorizing facts, students learn to collect data, use the scientific method, and apply this information to compose reports and ask questions.

Express complex meanings through writing. ...

Stay ahead of the curve in math classes.

Step-by-step explanation:

Answer:

Width: x - 5

Step-by-step explanation:

x² - 25

x² - 5²

(x - 5)(x + 5)

Step-by-step explanation:

Answer: ?

Step-by-step explanation:

Answer:

This is a parallelogram.

Step-by-step explanation:

This figure has two pairs of paralel sides with completely different angles.

Answer: 32.2

Step-by-step explanation:

If the value of x increases then the value of y decreases. Then the correct option is B.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

For the inverse variation function

[tex]\rm y = \dfrac{k}{x}[/tex]    (where x, k > 0),

We know that the y is inversely proportional to the x.

Thus, if the value of x increases then the value of y decreases.

Therefore, the correct option is B.

More about the function link is given below.

https://brainly.com/question/5245372

Answer:

Step-by-step explanation:

We are given with an equation in variable y and we need to solve for y . So , now let's start !!!

We are given with ;

[tex]{:\implies \quad \sf \dfrac{33}{2}+\dfrac{3y}{5}=\dfrac{7y}{10}+15}[/tex]

Take LCM on both sides :

[tex]{:\implies \quad \sf \dfrac{165+6y}{10}=\dfrac{7y+150}{10}}[/tex]

Multiplying both sides by 10 ;

[tex]{:\implies \quad \sf \cancel{10}\times \dfrac{165+6y}{\cancel{10}}=\cancel{10}\times \dfrac{7y+150}{\cancel{10}}}[/tex]

[tex]{:\implies \quad \sf 165+6y=7y+150}[/tex]

Can be further written as ;

[tex]{:\implies \quad \sf 7y+150=165+6y}[/tex]

Transposing 6y to LHS and 150 to RHS

[tex]{:\implies \quad \sf 7y-6y=165-150}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{y=15}}}[/tex]

Answer:

18

Step-by-step explanation:

Solve the question in steps

(8+36)/11

44/11=4

Now you have 4+7x2

You do multiplication first

4+14=18

Answer:

24 is your answer

Step-by-step explanation:

I first brought one side up as the other went down.

Then found the base and the side and added them all to get

8 as base and 4 multiply both by two then add to get 24

hope this helped.

A brainliest is always appreciated.

Answer:

y=-4

Step-by-step explanation: