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4 years ago

Which equation shows the commutative property of addition?

Mathematics

2 answers:

docker41 [41]4 years ago

6 0

Answer:

A-4+3=3+4

Step-by-step explanation:

The commutative property of addition, also known as the order property of addition, means that a given group of numbers can be added in any order and their sum will always be the same.

marishachu [46]4 years ago

3 0

Answer:

Step-by-step explanation:

commutative is where one equals out to another and then when using addition you have to use the plus sign

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Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph

Dennis_Churaev [7]

ANSWER TO QUESTION 1

$f(x)=(x-2)(x+3)(x-1)^2$ .

EXPLANATION

The function given to us is,

$f(x)=x^4-x^3-7x^2+13x-6$

According to rational roots theorem,

$\pm1,\pm2,\pm3,\pm6$ are possible rational zeros of

$f(x)=x^4-x^3-7x^2+13x-6$ .

We find out that,

$f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6$

$f(-3)=81+27-63-39-6$

$f(-3)=6-6$

$f(-3)=0$

Also

$f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6$

$f(2)=16-8-28+26-6$

$f(2)=6-6$

$f(2)=0$

This implies that

$x-2 and x+3$ are factors of

$f(x)=x^4-x^3-7x^2+13x-6$ and hence $(x-2)(x+3)=x^2+x-6$ is also a factor.

We perform the long division as shown in the diagram.

Hence,

$f(x)=(x-2)(x+3)(x-1)^2$ .

ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots

$x=2$ and $x=-3$ have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.

Also the root $x=1$ has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

$x\le -3$

$f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6$

$f(-4)=150\:>0$

$-3\le x \le 1$

$f(0)=-6\:$

$1\le x\le 2$

$f(1.5)=-0.56\:$

$x \ge 2$

$f(3)=24\:>0$

We can now use these information to sketch the function as shown in diagram

4 0

3 years ago

A lunch bill $12 before tax. If tax on the bill is 7.5%, what is the total cost of the lunch including tax?

Paladinen [302]

Answer:

$12.90

Step-by-step explanation:

To solve, multiply the cost before tax with tax, and then add the number gotten to the original amount.

12 x 7.5% = 12 x 0.075 = 0.9

12 + 0.9 = 12.9

$12.90 is your answer.

7 0

4 years ago

Read 2 more answers

A musical instrument has a pitch of 220 hertz when the wavelength is 3 feet. When the wavelength is 4 feet, the pitch is 165 her

ZanzabumX [31]

Answer:

239

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A car salesman had $65,100 in sales. He earned $1,953 in commission. What percent commission did he earn. Explain your answer.

ahrayia [7]

Answer:

1. The percent commission earned is 3%.

2. The loan period is 3.29 years.

Step-by-step explanation:

1. Salesman has $65,100 in sales. He earned $1,953 in commission.

Let the percent commission earn be x%

Therefore, x% of the sales equals $1,953

$\frac{x}{100} of $65,100 = $1,953$

$\frac{x}{100} * 65100 = 1953\\\frac{65100x}{100} = 1953$

We cross multiply

$\frac{65100x}{100} = 1953\\65100x = 1953 * 100\\65100x = 195300$

Divide both side by the coefficient of 'x' (65100)

$\frac{65100x}{65100} = \frac{195300}{65100} \\x = 3$

Therefore, the percent commission earned is 3%

2. Interest (I) = $299 Principal (P) = $1300 Rate (R) = 7%

The formula for finding interest is given as: $I = \frac{PRT}{100}$

Therefore, substituting into the formula, we have:

$299 = \frac{1300 * 7 * T}{100}$

We are finding the time it takes the loan to earn an interest of $299

$299 = \frac{1300 * 7 * T}{100} \\299 = \frac{9100T}{100}$

We cross-multiply:

$299 * 100 = 9100T\\29900 = 9100T$

Divide both side by the coefficient of T (9100)

$\frac{29900}{9100} = \frac{9100T}{9100}\\T = 3.29$

Therefore, the time taken for the loan to earn such interest is approximately 3.29 years

4 0

3 years ago

SOME ONEEE PLZZ HELPP MEEEE

Dominik [7]

Answer:

2.5

Step-by-step explanation:

The minimum value is the minimum y-value a function includes. In this case, since you can see the function is periodic (it repeats itself <em>periodically</em>, hence periodic) and the smallest y-value the function encounters is 2.5 (doesn't go below this value), the minimum y-value is 2.5. I hope this made sense. If not, feel free to let me know.

6 0

3 years ago