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2 years ago

Norris wrote the equation 7x9=63.Blake wrote the equation 7x9=9x7.Who wrote a correct equation?Explain

Mathematics

1 answer:

Karolina [17]2 years ago

7 0

Answer:

Step-by-step explanation:

They are both technically right 7 time 9 is 63 but 7 time 9 is equivalent to 9 times 7

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[50 pts] An even number, n, times the next consecutive number, n + 2, is equal to 168. Find the original number.

ale4655 [162]

We are given:

An even number 'n', multiplied by the next consecutive even number is 168

Solving for n:

From the given statement, we can say that:

n(n+2) = 168 [n multiplied by the next even number 'n+2']

n² + 2n = 168

n² + 2n - 168 = 0 [subtracting 168 from both sides]

We can see that we now have a quadratic equation, solving using splitting the middle term

n² + 14n - 12n - 168 = 0

n(n + 14) -12(n + 14) = 0 [factoring out common terms]

(n-12)(n+14) = 0

Here, we can divide both sides by either (n-12) OR (n+14)

Checking the result in both the cases:

(n + 14) = 0/(n-12) (n-12) = 0/(n+14)

n + 14 = 0 n - 12 = 0

n = -14 n = 12

Both these values are even and since we are not told if the number 'n' is positive or negative, both 12 and -14 are the possible values of n

4 0

2 years ago

HELPPP!!!!!!!!!!!!!!!!

Neko [114]

Answer:

Step-by-step explanation:

Because of the exponent in x²

5 0

2 years ago

30 points!! What is the sum of the first six terms of the series? 48 - 12 + 3 - 0.75 +...

Lunna [17]

Answer:

The sum of the first six terms is 38.39

Step-by-step explanation:

This is a geometric sequence since the common difference between each term is $-\frac{1}{4}$

Thus, $r=-\frac{1}{4}$

To find the sum of first six terms, we need to find the fifth and sixth term of the sequence.

To find the fifth term:

The general form of geometric sequence is $a_{n}=a_{1} \cdot r^{n-1}$

To find the fifth term, substitute $n=5$ in $a_{n}=a_{1} \cdot r^{n-1}$

$\begin{aligned}a_{5} &=(48) \cdot\left(-\frac{1}{4}\right)^{5-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{4} \\&=(48)\left(\frac{1}{256}\right) \\a_{5} &=0.1875\end{aligned}$

To find the sixth term, substitute $n=6$ in $a_{n}=a_{1} \cdot r^{n-1}$

$\begin{aligned}a_{6} &=(48) \cdot\left(-\frac{1}{4}\right)^{6-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{5} \\&=(48)\left(-\frac{1}{1024}\right) \\a_{5} &=-0.046875\end{aligned}$

To find the sum of the first six terms:

The general formula to find Sn for $|r|$ is $S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}$

$\begin{aligned}S_{6} &=\frac{48\left(1-\left(-\frac{1}{4}\right)^{6}\right)}{1-\left(-\frac{1}{4}\right)} \\&=\frac{48\left(1-\frac{1}{4096}\right)}{1+\frac{1}{4096}} \\&=\frac{48(0.95)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{47.9904}{5} \\&=38.39\end{aligned}$

Thus, the sum of first six terms is 38.39

5 0

2 years ago

MATH HOMEWORKKKKKKKKKKKKKKKKKKKKKKKK

BaLLatris [955]

20.9984 rounded = 21

6 0

2 years ago

11.Write the equations of linear and exponential functions that pass through the points (0,9) and (1,3)

Schach [20]

9514 1404 393

Answer:

y = -6x +9

y = 9·(1/3)^x

Step-by-step explanation:

In each case, the y-intercept is 9.

Linear

The slope is rise/run = (3-9)/(1-0) = -6, so the equation is ...

y = mx + b . . . . . . . slope m, intercept b

y = -6x +9

Exponential

The ratio of value at x=1 to that at x=0 is 3/9 = 1/3. That is the "growth factor," so the equation is ...

y = 9·(1/3)^x

7 0

3 years ago