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jasenka [17]
3 years ago
11

Solve for x in the equation 6x=42

Mathematics
1 answer:
Sophie [7]3 years ago
8 0

Answer:

x=7

Step-by-step explanation:

6x=42

divide 6 on both sides

x=42/6

x=7

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Which of the following is a solution of y + x < -5?
dedylja [7]

Answer:

(-4, -2)

Step-by-step explanation:

To find if a point is a solution (or verifies) an inequation (or an equation), you simply have to enter the given values in it and see if it's true.

Let's try with all the 4 given choices:

(-4, -2)  

y + x < -5

-4 - 2 < -5

-6 < -5 TRUE

(-3, -2)

y + x < -5

-3 - 2 < -5

-5 < -5 FALSE

(-2, -3)

-2 - 3 < -5

-5 < -5 FALSE

(-1, -3)

-1 - 3 < -5

-4 < -5 FALSE

6 0
3 years ago
Find an m &gt; 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.
Aleonysh [2.5K]

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

x^4-(3m+2)x^2+m^2=0

x^4+0x^3-(3m+2)x^2+0x+m^2=0

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}

=\frac{0}{1}=0

\implies a=0----(1)

(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}

=\frac{-3m-2}{1}

3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2

-10b^2=-3m-2

\implies b^2=\frac{3m+2}{10}-----(2)

(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2

9b^4=m^2

9(\frac{3m+2}{10})^2=m^2

9(\frac{9m^2+4+12m}{100})=m^2

81m^2+36+108m=100m^2

-19m^2+108m+36=0

19m^2-108m-36=0

19m^2-114m+6m-36=0

19m(m-6)+6(m-6)=0

(19m+6)(m-6)=0

\implies m=-\frac{6}{19}\text{ or }m=6

But m > 0,

Hence, the value of m is 6.

4 0
3 years ago
A cyclist travels 5.8 km in 30 minutes. <br> What is his average speed in km/h?
Sauron [17]

Answer:

11.6km/h

Step-by-step explanation:

multiply 30 min by 2 to get to an hour

multiply 5.8 by 2 to get to km per hour

4 0
3 years ago
Read 2 more answers
In the image below, ABC ~ DEF What is the length of EF and the measure of D
Gwar [14]
If triangle ABC is congruent to triangle DEF, then EF = BC = 27
This is because BC and EF are the last two letters of ABC and DEF respectively. They match up and correspond, being congruent by CPCTC

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

Similarly, if triangle ABC is congruent to triangle DEF, then angle D = angle A = 49 degrees

The letter D and the letter A are the first letters of DEF and ABC respectively. So they match up and are congruent by CPCTC

CPCTC = Corresponding Parts of Congruent Triangles are Congruent

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

So in short, the answer is choice B) 27; 49

7 0
3 years ago
Nth Term help please
liberstina [14]

\bf \begin{array}{|ll|ll} \cline{1-2} term&value\\ \cline{1-2} a_1&3\\[0.8em] a_2&\stackrel{3\cdot 2}{6}\\[0.8em] a_3&\stackrel{6\cdot 2}{12}\\[0.8em] a_4&\stackrel{12\cdot 2}{24}\\[0.8em] a_5&\stackrel{24\cdot 2}{48}\\[0.8em] a_6&\stackrel{48\cdot 2}{96} \\ \cline{1-2} \end{array}

8 0
3 years ago
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