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vladimir1956 [14]

3 years ago

12

The area of a rectangle is given by the expression x^2+5x+4. If the length of one side is given by x+2, what is the length of th

e other side?

2 answers:

SVEN [57.7K]3 years ago

6 0

Answer:

10

Step-by-step explanation:

5 =4 times square root of 2

Charra [1.4K]3 years ago

5 0

5=4 Times Square root of 2 answer: 10

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cluponka [151]

Answer:

c

Step-by-step explanation:

3 0

3 years ago

Consider the two functions:

koban [17]

Answer:

a) The x value of the point where the two equations intersect in terms of a is $x=\frac{40}{4+5a}$

b) The value of the functions at the point where they intersect is $\frac{10 (28 + 15 a)}{4 + 5 a}$

c) The partial derivative of f with respect to $x$ is $\frac{\partial f}{\partial x} = -5a$ and the partial derivative of f with respect to $a$ is $\frac{\partial f}{\partial x} = -5x$

d) The value of $\frac{\partial f}{\partial x}(3,2) = -10$ and $\frac{\partial f}{\partial a}(3,2) = -15$

e) $\upsilon_1=-\frac{3}{4} = -0.75$ and $\upsilon_2=-\frac{3}{4} = -0.75$

f) equation $\upsilon_1 = \frac{-5a\cdot x}{70-5ax}=\frac{ax}{ax-14}$ and $\upsilon_2 = \frac{-5a\cdot a}{70-5ax}=\frac{a^2}{ax-14}$

Step-by-step explanation:

a) In order to find the $x$ we just need to equal the equations and solve for $x$ :

$f(x,a)=g(x)\\70-5xa = 30+4x\\70-30 = 4x+5xa\\40 = x(4+5a)\\\boxed {x = \frac{40}{4+5a}}$

b) Since we need to find the value of the function in the intersection point we just need to substitute the result from a) in one of the functions. As a sanity check , I will do it in both and the value (in terms of $a$ ) must be the same.

$f(x,a)=70-5ax\\f(\frac{40}{4+5a}, a) = 70-5\cdot a \cdot \frac{40}{4+5a}\\f(\frac{40}{4+5a}, a) = 70 - \frac{200a}{4+5a}\\f(\frac{40}{4+5a}, a) = \frac{70(4+5a) -200a}{4+5a}\\f(\frac{40}{4+5a}, a) =\frac{280+350a-200a}{4+5a}\\\boxed{ f(\frac{40}{4+5a}, a) =\frac{10(28+15a)}{4+5a}}$

and for $g(x)$ :

$g(x)=30+4x\\g(\frac{40}{4+5a})=30+4\cdot \frac{40}{4+5a}\\g(\frac{40}{4+5a})=\frac{30(4+5a)+80}{4+5a}\\g(\frac{40}{4+5a})=\frac{120+150a+80}{4+5a}\\\boxed {g(\frac{40}{4+5a})=\frac{10(28+15a)}{4+5a}}$

c) $\frac{\partial f}{\partial x} = (70-5xa)^{'}=70^{'} - \frac{\partial (5xa)}{\partial x}=0-5a\\\frac{\partial f}{\partial x} =-5a$

$\frac{\partial f}{\partial a} = (70-5xa)^{'}=70^{'} - \frac{\partial (5xa)}{\partial a}=0-5x\\\frac{\partial f}{\partial a} =-5x$

d) Then evaluating:

$\frac{\partial f}{\partial x} =-5a\\\frac{\partial f}{\partial x} =-5\cdot 2=-10$

$\frac{\partial f}{\partial a} =-5x\\\frac{\partial f}{\partial a} =-5\cdot 3=-15$

e) Substituting the corresponding values:

$\upsilon_1 = \frac{\partial f(3,2)}{\partial x}\cdot \frac{3}{f(3,2)} \\\upsilon_1 = -10 \cdot \frac{3}{40} = -\frac{3}{4} = -0.75$

$\upsilon_2 = \frac{\partial f(3,2)}{\partial a}\cdot \frac{3}{f(3,2)} \\\upsilon_2 = -15 \cdot \frac{2}{40} = -\frac{3}{4} = -0.75$

f) Writing the equations:

$\upsilon_1=\frac{\partial f (x,a)}{\partial x}\cdot \frac{x}{f(x,a)}\\\upsilon_1=-5a\cdot \frac{x}{70-5xa}\\\upsilon_1=\frac{-5ax}{70-5ax}=\frac{-5ax}{-5(ax-14)}\\\boxed{\upsilon_1=\frac{ax}{ax-14} }$

$\upsilon_2=\frac{\partial f (x,a)}{\partial x}\cdot \frac{a}{f(x,a)}\\\upsilon_2=-5a\cdot \frac{a}{70-5xa}\\\upsilon_2=\frac{-5a^2}{70-5ax}=\frac{-5a^2}{-5(ax-14)}\\\boxed{\upsilon_2=\frac{a^2}{ax-14} }$

8 0

4 years ago

Find the measure of x that would make m∥n.

Lisa [10]

Answer:

to get the value of xtake 4x + 2x + 36 degrees is equals to 180 degrees this is because 4X and 2x + 36 degrees are angles on a straight line because 4X corresponds to the angle on top of 2x + 36 degrees so back to the equation we collect the like terms it will be 4 x + 2 x is equals to 180 degrees minus 36 degrees 6 x is equals to 144 x is equals to 24 degrees

3 0

4 years ago

The original selling price of a single share of stock was d dollars. The selling price for a share of the same stock on a later

stepladder [879]

Answer:

A

Step-by-step explanation:

The expression 1.25 d means 100% of the price +25% of the price. This means it increased by 25%. Multiplying it by 0.8 means it's value is only 80% of the value now which means it must of had a 20% decrease after increasing. It's now at it's original price.

4 0

3 years ago

I need help on both of these please///:(

SCORPION-xisa [38]

14. The distance between the two points is 14.866.

Distance can be calculated with the following formula:

d=√(x₂-x₁)²+(y₂-y₁)²

d=√(12-2)²+(5-(-6))²

d=√10²+11²

d=√100+121

d=√221

d=14.866

15. The distance between the two points is 20.248.

Use the same formula to find the distance.

d=√(x₂-x₁)²+(y₂-y₁)²

d=√(4-(-3))²+(12-(-7))²

d=√7²+19²

d=√49+361

d=√410

d=20.248

4 0

4 years ago