Which of the following represents a pyramidal number sequence?

Complete the sentence below. If (3x2 + 22x + 7) ÷(x + 7) = 3x + 1, then (x + 7)(???????) =???? .

g100num [7]

Answer: The answer is $(x+7)(3x+1)=33x^2+22x+7.$

Step-by-step explanation: Given that

$(3x2 + 22x + 7) \div(x + 7) = 3x + 1,$

and we are to complete the following sentence:

$(x+7)(???)=???$

We have the following division algorithm for polynomials

$\textup{If }a(x)\times b(x)=c(x),\\\textup{then, we have }\\\\\dfrac{c(x)}{b(x)}=a(x)~~~~~\textup{or}~~~~~~c(x)\div b(x)=a(x).$

Here, a(x) = quotient, b(x) = divisor and c(x) = dividend.

Applying this rule in the given problem, we have

$\textup{since }(3x2 + 22x + 7) \div(x + 7) = 3x + 1,\\\\\textup{so, }\\\\(x+7)(3x+1)=3x^2+22x+7=0.$

Thus, the complete sentence is

$(x+7)(3x+1)=3x^2+22x+7=0.$

7 0

2 years ago

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The vertex of this parabola is at (2,-4). When the y value is -3, the x-value is

marusya05 [52]

$\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} h=2\\ k=-4 \end{cases}\implies y=a(x-2)^2-4 \\\\\\ \textit{we also know that } \begin{cases} y = -3\\ x = -3 \end{cases}\implies -3=a(-3-2)^2-4\implies 1=a(-5)^2 \\\\\\ 1=25a\implies \boxed{\cfrac{1}{25}=a}$

4 0

2 years ago

The formula for the future value V (in dollars) of an investment earning simple interest is V=p+prt, where p (in dollars) is the

zhannawk [14.2K]

a)

V=p+prt

now we solve for P

V=P (1+rt)

Divide both sides by (1+rt)

P=V÷(1+rt)...answer

b)

P=V÷(1+rt)

P=3,000÷(1+0.06×5)

P=2,307.69

5 0

2 years ago

The table shows Mr. Winkler’s schedule for paying off his credit card balance. A 5-column table with 4 rows. Column 1 is labeled

statuscvo [17]

Answer:

3

Step-by-step explanation:

6 0

2 years ago

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Sherri saves nickels and dimes in a coin purse for her daughter. The total value of the coins in the purse is $0.95. The number

forsale [732]

I’m guessing that this is for systems of equations?
n - nickels
d - dimes

These are the equations you start off with.
n = 5d-2
0.95 = 0.10d+0.05n

Substitute the top equation for n into the variable n in the bottom equation.
0.95 = 0.10d+0.05(5d-2)

Solve for d.
0.95 = 0.10d+0.25d-0.10
1.05 = 0.35d
3 = d

Substitute d into the top equation and solve for n.
n = 5(3)-2
n = 15-3
n = 12

There are 3 dimes and 12 nickels in the coin purse! Hope this helped <3

7 0

2 years ago

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