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2 years ago

Which of the following is equal to the absolute value of 7?

Mathematics

1 answer:

erastovalidia [21]2 years ago

6 0

A, as absolute value refers to distance a number is from 0 whether it be neg or pos

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The gas mileage for a certain vehicle can be approximated by m=−0.05x2+3.5x−49, where x is the speed of the vehicle in mph. Dete

Whitepunk [10]

Answer:

Step-by-step explanation:

Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;

m = −0.05x²+3.5x−49

when m= 9

9 = −0.05x²+3.5x−49

−0.05x²+3.5x−49 = 9

0.05x²-3.5x+49 = -9

Multiplying through by 100

5x²+350x−4900 = 900

Dividing through by 5;

x²+70x−980 = 180

x²+70x−980 - 180 = 0

x²+70x−1160 = 0

Using the general formula to get x;

a = 1, b = 70, c = -1160

x = -70±√70²-4(1)(-1160)/2

x = -70±√4900+4640)/2

x = -70±(√4900+4640)/2

x = -70±√9540/2

x = -70±97.7/2

x = -70+97.7/2

x = 27.7/2

x = 13.85mph

x ≈ 14 mph

Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph

4 0

2 years ago

Simplify ech answer into a fraction, Show all work please!

Gnom [1K]

Answer:

the first one is -9/40. the second one is 109/20. the third one is -8/35.

Step-by-step explanation:

here is the work for the first one 3/8-.6 and convert into a simplified fraction and came up with -9/40. here is the work for the second one 4 4/3+0.7 and then convert into a simplified fraction and came up with 109/20. here is the work for the third one 4/7-0.8 and then convert into a simplified fraction and came up with -8/35.

6 0

3 years ago

Alguien que hable español

NeX [460]

Answer:

Question it in english

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

PLEASE HELP AND ANSWER!!!!! Which of the following reveals the minimum value for the equation 2x2 + 12x − 14 = 0?

NARA [144]

Answer:

The correct option is 3.

Step-by-step explanation:

The given equation is

$2x^2+12x-14=0$

It can be written as

$(2x^2+12x)-14=0$

Taking out the common factor form the parenthesis.

$2(x^2+6x)-14=0$

If an expression is defined as $x^2+bx$ then we add $(\frac{b}{2})^2$ to make it perfect square.

In the above equation b=6.

Add and subtract 3^2 in the parenthesis.

$2(x^2+6x+3^2-3^2)-14=0$

$2(x^2+6x+3^2)-2(3^2)-14=0$

$2(x+3)^2-18-14=0$

$2(x+3)^2-32=0$ .... (1)

Add 32 on both sides.

$2(x+3)^2=32$

The vertex from of a parabola is

$p(x)=a(x-h)^2+k$ .... (2)

If a>0, then k is minimum value at x=h.

From (1) and (2) in is clear that a=2, h=-3 and k=-32. It means the minimum value is -32 at x=-3.

The equation $2(x+3)^2=32$ reveals the minimum value for the given equation.

Therefore the correct option is 3.

5 0

3 years ago

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. (If the ve

djyliett [7]

We're looking for $f(x,y,z)$ such that $\nabla f(x,y,z)=\vec F(x,y,z)$ , which requires

$\dfrac{\partial f}{\partial x}=xyz^2$

$\dfrac{\partial f}{\partial y}=x^9yz^2$

$\dfrac{\partial f}{\partial z}=x^9y^2z$

Integrating both sides of the first PDE wrt $x$ gives

$f(x,y,z)=\dfrac12x^2yz^2+g(y,z)$

Differenting this wrt $y$ gives

$\dfrac{\partial f}{\partial y}=x^9yz^2=\dfrac12x^2z^2+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=\dfrac12x^2z^2(2x^7y-1)$

but we're assuming $g(y,z)$ is a function that doesn't depend on $x$ , which is contradicted by this result, and so there is no such $f$ and $\vec F$ is not conservative.

8 0

3 years ago