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3 years ago

Simplify each expression 1.) (7+x) + 7x Pls show your work

1 answer:

8 0

The answer is 14x.

You always have to do whats in the parenthesis first. In this case you would do 7 + x = 7x. Then, you add this 7x to the other 7 x. 7x+7x=14x.

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Find the volume of the solid under the plane 5x + 9y − z = 0 and above the region bounded by y = x and y = x4.

svp [43]

<span>For the plane, we have z = 5x + 9y

For the region, we first find its boundary curves' points of intersection.
x = x^4 ==> x = 0, 1.

Since x > x^4 for y in [0, 1],

The volume of the solid equals

$\int\limits^1_0 { \int\limits_{x^4}^x {(5x+9y)} \, dy } \, dx = \int\limits^1_0 {\left[5xy+ \frac{9}{2} y^2\right]_{x^4}^{x}} \, dx \\ \\ =\int\limits^1_0 {\left[\left(5x(x)+ \frac{9}{2} (x)^2\right)-\left(5x(x^4)+ \frac{9}{2} (x^4)^2\right)\right]} \, dx \\ \\ =\int\limits^1_0 {\left(5x^2+ \frac{9}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx =\int\limits^1_0 {\left( \frac{19}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx \\ \\ =\left[ \frac{19}{6} x^3- \frac{5}{6} x^6- \frac{1}{2} x^9\right]^1_0$

$=\frac{19}{6} - \frac{5}{6} - \frac{1}{2} =\bold{ \frac{11}{6} \ cubic \ units}$ </span>

8 0

2 years ago

What is simplify 5+3-9

sergij07 [2.7K]

Answer:

-1

Step-by-step explanation:

first 5+3=8

8-9=-1

6 0

2 years ago

The table shows the temperature (y) at different altitudes (x).

Shtirlitz [24]

Answer/Step-by-step explanation:

2. Using two pairs of values, (0, 59) and (2,000, 51),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{51 - 59}{2,000 - 0} = \frac{-8}{2,000} = -\frac{1}{250}$

3. The y-intercept is the value of y when x = 0. Thus, x = 0, when y = 59. Therefore,

y-intercept (b) = 59

4. To write an equation in slope-intercept form, simply substitute m = -¹/250, and b = 59, in $y = mx + b$

✅ $y = -\frac{1}{250}x + 59$

5. Substitute x = 5,000 in $y = -\frac{1}{250}x + 59$ .

$y = -\frac{1}{250}(5,000) + 59$

$y = -20 + 59$

$y = 39$

At an altitude of 5,000 ft, temperature would be 39°F

3 0

2 years ago

Number when multiplied by 0.5?<br> Which number produces a rational

Vladimir79 [104]

I don’t really know what your asking but anything multiplied by 0.5 or .5 is going to be half of that number
Example 2•.5=1

I don’t know if this is what you were asking, but I hope this helps

6 0

2 years ago

Work out 12+8÷(9-5) 0.018÷0.06 Express as single fraction 5/7÷2/5

Anettt [7]

Step-by-step explanation:

I don't know if the first set of numbers is all in one set, but I'll do my best to give you an answer.

Really all you need to do is use PEMDAS for the first question.

(Parentheses, exponents, multiply, divide, add, subtract. In that order)

$1 2 + 8 \div (9 - 5) \\ 12 + 8 \div 4 \\ 12 + 2 \\ 14$