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3 years ago

Simplify the expression: 4x+2+12x+17

Mathematics

2 answers:

Anna71 [15]3 years ago

8 0

4x + 2 + 12x + 17

= 4x + 12x + 2 + 17

= 16x + 19

abruzzese [7]3 years ago

3 0

Answer:

$4x + 2 + 12x + 17 \\ = (4 + 12)x + (2 + 17) \\ = 16x + 19$

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Tracey has 29 students in her class. She has 21 boys in her class. What is the ratio of girls to boys in her class

Xelga [282]

First find the number of girls in her class.

29 student - 21 boys = 8 girls

So, the ratio of girls to boys is:

8 girls:21 boys

Or just:

8:21

answer: 8:21

6 0

4 years ago

Quadrilateral ABCD is inscribed in this circle.

Ilya [14]

Hello,

When you have an inscribed quadrilateral, the opposite sides are supplementary.

So you can write and solve the following equation.
x + 6x + 19 = 180
7x + 19 = 180
7x = 161
x = 23

Now, plug in 23 for X and we will find the measurement of B.
6(23) + 19
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The measure of angle B is 157 degrees. (The picture is not drawn to scale)

Good luck,
MrEQ

3 0

3 years ago

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$