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2 months ago

2.4 puzzle time how can you share five apples with seven friends

Mathematics

1 answer:

Svet_ta [12.7K]2 months ago

6 0

1. The algebraic equality property shown here is the multiplication property, corresponding to letter P.

2. The subtraction property of equality is represented here, answer E.

3. This demonstrates the substitution property of equality, answer M.

4. The division property of equality is depicted, answer A.

5. The addition property of equality is illustrated, answer A.

6. This shows the distributive property, answer E.

7. The transitive property of equality applies here, answer E.

8. The symmetric property of equality is represented, answer A.

9. The reflexive property of equality is shown, answer C.

10. This again depicts the multiplication property, answer P.

11. The subtraction property of equality is shown here, answer L.

12. The reflexive property of equality, answer S.

13. Demonstrates the transitive property, answer U.

14. Displays the symmetric property, answer K.

The numbers given are: 3 5 14 2
4 1 10 11 6 12 8 13 9 7

Using the letters corresponding to each number forms the phrase MAKE APPLESAUCE.

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Consider this system of equations. Which shows the second equation written in slope-intercept form? y = 3 x minus 2. 10 (x + thr

Leona [12618]

Question

Consider this system of equations. Which shows the second equation written in slope-intercept form?

$y = 3x - 2.$

$10(x + \frac{3}{5} ) = 2y$

A. $y = 5x + \frac{3}{10}$

B. $y = 5x + 3$

C. $y = \frac{1}{5} x + \frac{3}{25}$

D. $y = \frac{1}{2} x + 6$

Response:

B. $y = 5x + 3$

Detailed explanation:

Given

Equation 1: $y = 3x - 2.$

Equation 2: $10(x + \frac{3}{5} ) = 2y$

Required:

Equivalent of equation 2

To achieve an equivalence of equation 2 (in slope-intercept form), we must first simplify it

$10(x + \frac{3}{5} ) = 2y$

Open the brackets

$10*x + 10 *\frac{3}{5} = 2y$

$10x + \frac{30}{5} = 2y$

Simplify the fractions

$10x + 6 = 2y$

Divide by 2

$\frac{10x}{2} + \frac{6}{2} = \frac{2y}{2}$

$5x + 3 = y$

Re-arrange

$y = 5x + 3$

Next, we compare options A through D with $y = 5x + 3$

A. is not equal to $y = 5x + 3$

Next, we check the second option

$y = 5x + 3$ matches $y = 5x + 3$

This option represents the second equation in slope-intercept format.

We check for further options

$y = \frac{1}{5} x + \frac{3}{25}$

Convert the fraction into a decimal

$y = 0.2x + 0.12$

This does not equal $y = 5x + 3$

$y = \frac{1}{2} x + 6$

Convert the fraction to decimal

$y = 0.5x + 6$

This also does not equal to $y = 5x + 3$

Therefore, the only option equivalent to the second equation in slope-intercept form is Option B

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23 days ago

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If mJI = (3x+2)°, mHLK = (15x-36)°, and m∠HML = (8x-1)°, find mHLK

lawyer [12517]

Response:

The measure of mHLK is "(204)°".

Step-by-step breakdown:

Given values include:

mJI = (3x+2)°

mHLK = (15x-36)°

and,

m∠HML = (8x-1)°

then,

What is mHLK?

Now,

Utilizing the chord-chord angle formula, we find

$mHMK=\frac{1}{2}(mJL+mHLK)$

Inserting the known values into the equation gives us

⇒ $(8x-1)=\frac{1}{2}(15x-36+3x+2)$

By carrying out cross-multiplication, we arrive at

⇒ $2(8x-1)=18x-34$

⇒ $16x-2=18x-34$

By subtracting "18x" from both sides, we obtain

⇒ $16x-2-18x=18x-34-18x$

⇒ $-2x-2=-34$

Upon adding "2" to both sides, we end up with

⇒ $-2x=-34+2$

⇒ $-2x=-32$

⇒ $x=\frac{32}{2}$

⇒ $x=16$

By substituting the value of "x" into mHLK = (15x-36)°, we calculate

⇒ (15x-36)° = (15×16-36)°

⇒ = (240-36)°

⇒ = (204)°

Thus, mHLK = (204)°

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