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2 years ago

The sum of a number, n, and 8 is multiplied by -4, and the result is -12.

Mathematics

1 answer:

forsale [732]2 years ago

4 0

Step-by-step explanation:

The number n is - 5

Because the sum = 8 + (-5) = 3

After multiply by - 4 = 3 x - 4 = - 12

Option A is the correct answer

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PLEASE HELP ASAP<br> Prove that x+a is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5

Brums [2.3K]

$P(x)=(x+a)^5 + (x+c)^5 + (a-c)^5$

If $x+a$ is a factor of $P(x)$ , then $-a$ is a root of $P(x)$ .

Therefore

$(-a+a)^5+(-a+c)^5+(a-c)^5=0\\\\0^5+(-1(a-c))^5+(a-c)^5=0\\\\(-1)^5(a-c)^5+(a-c)^5=0\\\\-(a-c)^5+(a-c)^5=0\\\\0=0$

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2 years ago

Determine the mean of the following numbers: 28,40,53,39,45

Nuetrik [128]

Answer:

Step-by-step explanation:

add all numbers together then divide by how many numbers there are

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1 year ago

Read 2 more answers

Labrador Retriever weighs 48 kg after a diet and exercise program the dog weighs 43 kilograms to determine if this shows a perce

ExtremeBDS [4]

Answer:

percentage change in weight ≈ 10%

Step-by-step explanation:

The dog weighed 48 kg after a diet and after an exercise program the dog had a weight of 43 kg. This means the dog loss weight since the dog weight decreased from an initial value of 48 kg to 43 kg. The decrease in weight can be calculate as

decrease in weight = original weight - new weight

original weight = 48 kg

new weight = 43 kg

decrease in weight = 48 - 43 = 5 kg

Since the weight decrease their will be a percentage decrease in weight.

% decrease = decrease in weight/original weight × 100

% decrease = 5/48 × 100

% decrease = 500/48

% decrease = 10. 42666666667

percentage change in weight ≈ 10%

5 0

1 year ago

the cross sectional area of a cylinder is 614 cm 2 the height is 8cm what is the volume of the cylinder

Elina [12.6K]

Answer: Volume of the cylinder = $4912\ cm^2$

Step-by-step explanation:

Volume of cylinder = Area of base x height

Also, area of cross section = Area of base

Volume of cylinder = area of cross section x height

Given: Area of cross section = $614\ cm^2$

height = 8 cm

Volume of cylinder = 614 x 8

$= 4912 \ cm^2$

Hence, the volume of the cylinder = $4912\ cm^2$

6 0

1 year ago

Find the point (x,y) of x2+14xy+49y2=100 that is closest to the origin and lies in the first quadrant.

Gala2k [10]

Notice that

$x^2+14xy+49y^2=(x+7y)^2$

so the constraint is a set of two lines,

$(x+7y)^2=100\implies\begin{cases}x+7y=10\\x+7y=10\end{cases}$

and only the first line passes through the first quadrant.

The distance between any point $(x,y)$ in the plane is $\sqrt{x^2+y^2}$ , but we know that $\sqrt{f(x,y)}$ and $f(x,y)$ share the same critical points, so we need only worry about minimizing $x^2+y^2$ . The Lagrangian for this problem is then

$L(x,y,\lambda)=x^2+y^2+\lambda(x+7y-10)$

with partial derivatives (set equal to 0)

$L_x=2x+\lambda=0$

$L_y=2y+7\lambda=0$

$L_\lambda=x+7y-10=0$

We have

$L_y-7L_x=2y-14x=0\implies y=7x$

which tells us that

$x+7y-10=0\iff x+49x=10\implies x=\dfrac15\implies y=\dfrac75$

so that $\left(\dfrac15,\dfrac75\right)$ is a critical point. The Hessian for the target function $x^2+y^2$ is

$H(x,y)=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite for all $x,y$ , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is $\sqrt{\left(\dfrac15\right)^2+\left(\dfrac75\right)^2}=2$ .

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2 years ago