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3 years ago

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

Mathematics

2 answers:

g100num [7]3 years ago

7 0

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

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

svetoff [14.1K]3 years ago

3 0

Answer:

3x+1, 3x^2+22x+7, and closure

Step-by-step explanation:

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The difference between the highest and lowest score in a distribution

trasher [3.6K]

Answer:

Range

Step-by-step explanation:

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3 years ago

A jar contains only quarters and dimes. The jar contains a total of 92 coins. The value of all the coins is 14$. How many quarte

skad [1K]

Answer:

read the explanation ya bean bag

Step-by-step explanation:

we can set up some equations

lets say that q=one quarter and d=one dime

there are 92 coins so q+d=92

for each quarter, there are 25 cents added towards the 14 dollars

for each dime, there are 10 cents added towards the 14 dollars

14 dollars is equal to 1400 cents

using all this information, we can write the following equation:

25q+10d=1400

we can simplify this to 5q+2d=280

remember that q+d=92, so let's take out the extra dimes: 3q+2(q+d)=280 or 3q+2*92=280 or 3q+184=280 or 3q=96 or q=32

there are 32 quarters, so we can subtract 32 from 92 to figure out how many dimes we have

92-32=60 dimes

6 0

3 years ago

Write the equation of the line with x-intercept -2 and y-intercept -1 in slope-intercept form

eduard

The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.

Now that we have two points, we can solve for slope m

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Given two points} \\ (-2,0)\rightarrow(x_1,y_1) \\ (0,-1)\rightarrow(x_2,y_2) \\ \\ \text{Substitute} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-0}{0-(-2)} \\ m=-\frac{1}{2} \end{gathered}$

Now that we have both m and b. Substitute these values to the slope intercept form

$\begin{gathered} \text{Slope intercept form is} \\ y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ \text{Substitute the values from before and we get} \\ y=-\frac{1}{2}x-1 \end{gathered}$

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1 year ago

The cost of a car rental is $35 per day plus 21 cents per mile. You are on a daily budget of $98. Write and solve an inequalit

erma4kov [3.2K]

Let x = mileage
98 >= 35 + .21x
Solving for x:
98 >= 35 + .21x
63 >= .21x
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2 years ago

7(2+3x)+8, 12+3(8+x), and (7x+2)3+8x

suter [353]

Answer:

The first answer is 21x+22.

Second answer is 36+3x.

Third answer is 29x+6.

Step-by-step explanation:

I just simplified

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2 years ago