In the diagram, lines JK and LM at N, M MNK = 2x + 30.<br> What is the value of x?

Estimate this product by rounding each number to one nonzero digit before multiplying: (2876)(513)(18) ASAP PLEASE

DerKrebs [107]

2876 Rounds To 3000
513 Rounds To 500
18 Rounds To 20
Then multiply:
3000x500x20= 30,000,000

Hope i helped :)

5 0

3 years ago

What is the quotient when 4x3 + 2x + 7 is divided by x + 3?

Arte-miy333 [17]

Answer:

The quotient of this division is $(4x^2 -12x + 38)$ . The remainder here would be $-26$ .

Step-by-step explanation:

The numerator $4x^3 + 2x + 7$ is a polynomial about $x$ with degree $3$ .

The divisor $x + 3$ is a polynomial, also about $x$ , but with degree $1$ .

By the division algorithm, the quotient should be of degree $3 - 1 = 2$ , while the remainder shall be of degree $1 - 1 = 0$ (i.e., the remainder would be a constant.) Let the quotient be $a\,x^2 + b\, x + c$ with coefficients $a$ , $b$ , and $c$ .

$4x^3 + 2x + 7 = \left(a\,x^2 + b\, x + c\right)(x + 3)$ .

Start by finding the first coefficient of the quotient.

The degree-three term on the left-hand side is $4 x^3$ . On the right-hand side, that would be $a\, x^3$ . Hence $a = 4$ .

Now, given that $a = 4$ , rewrite the right-hand side:

$\begin{aligned}&\left(4\,x^2 + b\, x + c\right)(x + 3) \cr =& \left(4x^2 + (b\, x + c)\right)(x + 3) \cr =& 4x^2(x + 3) + (bx + c)(x + 3) \cr =& 4x^3 + 12x^2 + (bx + c)(x + 3)\end{aligned}$ .

Hence:

$4x^3 + 2x + 7 = 4x^3 + 12x^2 + (b\,x + c)(x + 3)$

Subtract $\left(4x^3 + 12x^2\right$ from both sides of the equation:

$-12x^2 + 2x + 7 = (b\,x + c)(x + 3)$ .

The term with a degree of two on the left-hand side has coefficient $(-12)$ . Since the only term on the right hand side with degree two would have coefficient $b$ , $b = -12$ .

Again, rewrite the right-hand side:

$\begin{aligned}&\left(-12 x + c\right)(x + 3) \cr =& \left(-12 x+ c\right)(x + 3) \cr =& (-12x)(x + 3) + c(x + 3) \cr =& -12x^2 -36x + (bx + c)(x + 3)\end{aligned}$ .

Subtract $-12x^2 -36x$ from both sides of the equation:

$38x + 7 = c(x + 3)$ .

By the same logic, $c = 38$ .

Hence the quotient would be $(4x^2 - 12x + 38)$ .

6 0

3 years ago

Express 24/40 and 18/42 in their simplest forms.Show your works

Maru [420]

Answer:

24/40 = 4/5

18/42 = 3/7

Step-by-step explanation:

Sana makatulong

7 0

3 years ago

Read 2 more answers

Can anyone help me out on this question?

svp [43]

Firstly , we will check continuity at x=1

we can use method

Suppose, f(x) is continuous at x=c

then it must satisfy

$\lim_{x \to c} f(x)=f(c)$

$\lim_{x \to 1} f(x)=f(1)$

firstly , we can find limit

$\lim_{x \to 1-} f(x)= \lim_{x \to 1-}(x+3)=1+3=4$

$\lim_{x \to 1+} f(x)= \lim_{x \to 1-}(3x+1)=3*1+1=4$

so, we get

$\lim_{x \to 1} f(x)= 4$

now, we can find f(1)

$f(1)=3*1+1=4$

so, we got

$\lim_{x \to 1} f(x)=f(1) =4$

so, this is continuous at x=1

Hence , option-D...........................Answer

5 0

3 years ago

Find the interest earned.

SCORPION-xisa [38]

June is 30 days
30-12=18 days
July is 31 days
August is 30 days
Time=18+31+30=79 days
A=2,750×(1+0.035÷365)^(79)
A=2,770.91
Interest earned
I=A-p
I=2770.91-2750
I==20.91

4 0

3 years ago

In the diagram, lines JK and LM at N, M MNK = 2x + 30. What is the value of x?