Solve the equation
- 1
- m - 7 = 5
3

Answers

Answer 1
Answer:

1/3m-7=5

One solution was found :

m = 36
Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

1/3*m-7-(5)=0

Step by step solution :

Step 1 :

1
Simplify —
3
Equation at the end of step 1 :

1
((— • m) - 7) - 5 = 0
3
Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a whole from a fraction

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

7 7 • 3
7 = — = —————
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

Adding fractions that have a common denominator :

2.2 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:

m - (7 • 3) m - 21
——————————— = ——————
3 3
Equation at the end of step 2 :

(m - 21)
———————— - 5 = 0
3
Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

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

5 5 • 3
5 = — = —————
1 3
Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

(m-21) - (5 • 3) m - 36
———————————————— = ——————
3 3
Equation at the end of step 3 :

m - 36
—————— = 0
3
Step 4 :

When a fraction equals zero :

4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

m-36
———— • 3 = 0 • 3
3
Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
m-36 = 0

Solving a Single Variable Equation :

4.2 Solve : m-36 = 0

Add 36 to both sides of the equation :
m = 36

One solution was found :

m = 36

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Graph the line that contains the point (-3,1) with a slope of 2/3

Answers

Answer:

The graph of the line that contains the point (-3,1) with a slope of 2/3.

Step-by-step explanation:

As the line contains the point (-3, 1) with a slop 2/3

Given the slop-intercept form of the line equation

y = mx+b

Here,

  • m = slope
  • b = y-intercept

Substituting the values in the slop-intercept form of the line equation

y = mx+b

1 = (2)/(3) (-3) + b

1 =- 2 + b

switching sides

-2+b=1

b=3

Now Substituting the value of b=3 in the slop-intercept form of the line equation

y = mx+b

y=(2)/(3) x+3

Hence, the line of the equation will be:  y=(2)/(3) x+3

Therefore, the graph of the line that contains the point (-3,1) with a slope of 2/3.

Using the unit circle, determine the value of sin 450°

Answers

Answer:

1

Step-by-step explanation:

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

Rotate ‘r’ anticlockwise to form a 90° or 450° angle with the positive x-axis.

The sin of 450 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

Hence the value of sin 450° = y = 1

Answer:

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

Simplify the expression
\sqrt[3]{686x {}^(4) } y {}^(7)

Answers

The expression can be simplified as  7x\sqrt[3]{ 2x} y^7.

What is an expression?

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

A phrase in language may contain an action on its own, but it does not constitute a whole sentence.

Given:

The expression = \sqrt[3]{686x^4} y^7

Factorize 686 we get 7³ × 2

= \sqrt[3]{7^3* 2x^4} y^7

= 7x\sqrt[3]{ 2x} y^7

Therefore, the expression can be simplified as  7x\sqrt[3]{ 2x} y^7.

To know more about the expression:

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Final answer:

The simplified form of the expression \sqrt[3]{686x {}^{4}} * y {}^{7} is 2y^7x * \sqrt[3]{x}. This is achieved by breaking down 686 into its prime factors and simplifying under the cube root.

Explanation:

To simplify the given expression \sqrt[3]{686x {}^{4} } y {}^{7}, we first break down 686 into its prime factors. 686 = 2 * 7 * 7 * 7 or 2 * 7^3. Now we can simplify the given expression by solving it inside the cube root first: \sqrt[3]{2 * 7^3 * x^4}, which simplifies to 2y^7x * \sqrt[3]{x}

\sqrt[3]{686x {}^{4}} * y {}^{7} = 2y^7x * \sqrt[3]{x}

Learn more about Solving Expressions here:

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A. Use your calculator to approximate ∫^ b_0 e^-0.00001x dx for b=10, 50, 100 and 1000.b. Based on your answers to part a, does ∫^[infinity]_0 e^-0.00001 dx appear to be convergent or divergent?
c. To what value does the integral actually converge?

Answers

Answer:

Step-by-step explanation:

We are to integrate the function

e^-0.00001x from 0 to b for different ascending values of x.

\int e^-0.00001x = -10^5 e^-0.00001x

Now we substitute the limits

When b =10

I = integral value = -10^5 e^-0.00001*10

b =50, I = -10^5(e^-0.00001*50-1)

b =100, I = -10^5( e^-0.00001*100-1)

b =1000 I=  -10^5 (e^-0.00001*1000-1)

b) As b increases exponent increases in negative, or denominator increases hence when b becomes large this will be a decreasing sequence hence converges

c) Converges to  -10^5 (0-1)=10^5

What is the solution to -4 (2x +6)=-24

Answers

Answer:

x=0

Step-by-step explanation:

Distribute -4

-8x - 24 = -24

Add 24 to both sides

-8x = 0

x=0

Answer:

x=0

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−4(2x+6)=−24

(−4)(2x)+(−4)(6)=−24(Distribute)

−8x+−24=−24

−8x−24=−24

Step 2: Add 24 to both sides.

−8x−24+24=−24+24

−8x=0

Step 3: Divide both sides by -8.

−8x

−8

=

0

−8

x=0

Answer:

x=0

One weekend Nate compared his history homework to his younger sister Caroline social studies homework he found out that for every 2 1/3 pages he had to read for homework Caroline how to read one page for homework how many pages did Nate read for every three pages that Caroline re One weekend Nate compared his history homework to his younger sister Caroline social studies homework he found out that for every 2 1/3 pages he had to read for homework Caroline had to read one page for homework how many pages did Nate read for every three pages that Caroline read

Answers

2 1/3 * 3 = 7

2*3=6 1/3*3=1

6+1 = 7