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3 years ago

What is the constant term in the expression 4xy + 8x +5?

Mathematics

1 answer:

expeople1 [14]3 years ago

8 0

Answer:

Step-by-step explanation:

The constant term is the one that has no variables :)

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With a full 12-gallon tank of fuel, Dillon’s car can travel about 420 miles. At that rate, about how far can Dillon’s car travel

Xelga [282]

175 miles~~~~~~~~~~~~

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4 years ago

Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to

goldenfox [79]

Find answers to the questions in the attached file.

Learn more about area of a regular hexagon: brainly.com/question/1601601

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2 years ago

Use the following information to answer all parts of question 3.3a: What is the area of the triangle? (Area of triangle = 1/2*b*

Anit [1.1K]

Answer:

See below ~

Step-by-step explanation:

3a : Area of the triangle

A = 1/2bh
A = 1/2 x 10 x 8
A = 5 x 8
A = 40 m²

3b : Area of the semicircle

Finding the radius (equal to 1/2 of the triangle hypotenuse)
Apply Pythagorean Theorem here
√8² + 10² = d
√64 + 100 = d
d = √164
d = 2√41
r = √41

A = πr²/2
A = 3.14 x (√41)² / 2
A = 1.57 x 41
A = 64.4 m² (nearest tenth)

5 0

2 years ago

I know you’re supposed to change the bounds and break up the integral, but for some reason, I can’t get the 44/3. Can someone ex

tatyana61 [14]

First, look for the zeroes of the integrand in the interval [0, 6] :

x² - 6x + 8 = (x - 4) (x - 2) = 0 ⇒ x = 2 and x = 4

Next, split up [0, 6] into sub-intervals starting at the zeroes we found. Then check the sign of x² - 6x + 8 for some test points in each sub-interval.

• For x in (0, 2), take x = 1. Then

x² - 6x + 8 = 1² - 6•1 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

• For x in (2, 4), take x = 3. Then

x² - 6x + 8 = 3² - 6•3 + 8 = -1 < 0

so x² - 6x + 8 < 0 over this sub-interval.

• For x in (4, 6), take x = 5. Then

x² - 6x + 8 = 5² - 6•5 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

Next, recall the definition of absolute value:

$|x| = \begin{cases}x & \text{for }x \ge0 \\ -x & \text{for }x < 0\end{cases}$

Then from our previous analysis, this definition tells us that

$|x^2 - 6x + 8| = \begin{cases}x^2 - 6x + 8 & \text{for }0$

So, in the integral, we have

$\displaystyle \int_0^6 |x^2-6x+8| \, dx = \left\{\int_0^2 - \int_2^4 + \int_4^6\right\} (x^2 - 6x + 8) \, dx$

Then

$\displaystyle \int_0^2 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_0^2 = \frac{20}3 - 0 = \frac{20}3$

$\displaystyle \int_2^4 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_2^4 = \frac{16}3 - \frac{20}3 = -\frac43$

$\displaystyle \int_4^6 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_4^6 = 12 - \frac{16}3 = \frac{20}3$

and the overall integral would be

20/3 - (-4/3) + 20/3 = 44/3

3 0

3 years ago

Find the equation of the linear function represented by the table below in slope-

Eva8 [605]

Answer:

f(x) = 5x - 5

Step-by-step explanation:

Let the equation of the linear function is,

f(x) = mx + b

Here, m = Slope of the graph

b = y-intercept

Slope of the line passing through $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

m = $\frac{(y_2-y_1)}{(x_2-x_1)}$

From the table attached,

Slope of the line passing through (2, 5) and (6, 25) will be,

m = $\frac{25-5}{6-2}$

m = 5

Equation of the linear function will be,

f(x) = 5x + b

Since, a point (10, 45) lies on the function,

45 = 5(10) + b

b = 45 - 50

b = -5

Equation of the linear function will be,

f(x) = 5x - 5

4 0

3 years ago