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3 years ago

Find the value for x.

Mathematics

2 answers:

jasenka [17]3 years ago

7 0

Answer:

x = 19

Step-by-step explanation:

5x = 3x +38

that means 2x = 38

x = 19

grigory [225]3 years ago

3 0

Answer:

x=19

Step-by-step explanation:

(3x+38)°=5x°(corresponding angles)

3x°+38°=5x°

38°=5x°-3x°

38°=2x°

38°/2°=2X°/2°

19=x

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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 $(4x^2 - 12x + 38)$ .

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4 years ago

A sequence is defined recursively by f(0)=2 and f(n)=f(n+1)=-2f(n)+3 for n greater than or equal to 0, then f(2) is equal to

kykrilka [37]

If you would like to know what is f(2), you can calculate this using the following steps:<span>

f(0) = 2
f(n+1) = - 2 * f(n) + 3
f(1) = - 2 * f(0) + 3 = - 2 * 2 + 3 = - 4 + 3 = - 1
f(2) = - 2 * f(1) + 3 = - 2 * (-1) + 3 = 2 + 3 = 5

The correct result would be f(2) = 5.</span>

4 0

4 years ago

A food truck operator is parked in a lot at the corner of two streets. She wants to be equidistant from both streets. Should she

alekssr [168]

Answer:

Angle bisector

Step-by-step explanation:

median isn't applicable in this case as the roads from the streets are inclined at an angle.

altitude refers to height which is also not applicable

The perpendicular bisector is the locust of points equidistant from two points,

in this question the street are not seen as points but as lines which forms an angle and the bisection of this angle forms a locus where she can park her car. If she parks her car anywhere on the angular bisector of the two streets, she would be at equal distance from both streets.

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4 years ago

A model spaceship costs $15.99before tax the tax on the model spaceship is 8% what is the total cost of the model spaceship roun

valina [46]

There are two ways to find the total with tax

Either you can do

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Since the second one requires less steps, it's easier to do that.

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The cost with tax is

$17.27

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